There is a famous story about Louis van Gaal from his time at Bayern Munich. Van Gaal had insisted from the start on two major protocols at team meals: players must eat in the same space every day and they must sit up straight. A few weeks later Van Gaal spotted Luca Toni slouched in his seat at lunch and began to shout across the canteen. When Toni took no notice Van Gaal marched across, grabbed him by the collar (he is 6ft 1in, Toni 6ft 3in) and yanked his centre-forward up and almost out of his seat before walking back to his lunch in silence. Nobody slouched after that. Least of all Toni, who left on a free transfer before the year was out.

There are plenty of these stories, from pants-dropping testicular displays at Bayern to the more refined domestic details. Van Gaal likes discipline. But how much? There are two forms of the word "you" in Dutch, the familiar and the formal. At home Van Gaal has always insisted his two daughters use the formal version when addressing him, even in private. Suddenly, the spectacle of Manchester United's first-team players calling their temporary manager "Ryan" during the hiatus between David Moyes's departure and Van Gaal's appointment feels like a holiday camp-ish intermission.

If there is a cartoonish element to the details of the Van Gaal myth – here he comes, this wild-eyed Don Quixote, gripped by the unreconciled obsessions of extreme discipline and creative attacking football – then this is also a deadly serious business for the world's most indebted football club, fatigued by the prospect of a season outside the elite and in real need of a post-Ferguson sense of direction. United have never had a foreign manager, the Irishman Frank O'Farrell aside. They have never appointed a manager anywhere near Van Gaal's 62 years of age. So why this one?

The obvious answer is that Van Gaal represents, in outline, the complete opposite of his predecessor. Indeed, from a distance it is tempting to conclude United have been swayed a little by the managerial rotation inflicted on the England team: foreign doesn't work, go English; nice doesn't work, go nasty. Moyes offered trophyless continuity with the promise of a long stay. And received opinion seems to be that Van Gaal represents the anti-David Moyes, not so much continuity or longevity, but a gold-standard track record and a sense of playing once again with the big boys.

It is a more nuanced succession, just as Moyes was a sentimental, oddly literal kind of continuity appointment. United has been managed by Scots for 75 of the past 100 years (it seems fairly likely they will never be managed by one again), but Moyes was only ever the most flattering, rootsy Glasgow-centred Ferguson-Busby facsimile. It is Van Gaal, José Mourinho and the well-travelled elite of European management who represent continuity. Ferguson broke up, bought in and sold off teams on a similar scale to the itinerant big beasts of European football through his own successive United eras. He just didn't have to move house to do it.

So to Van Gaal, whose career makes a fairly good case – according to Louis van Gaal at least – for existing in a class of one. In the past few days the word genius has been routinely bandied about. Sir Bobby Robson once called him "the top of the tree". "He is a genius, the best I've ever seen on a training pitch," Mehmet Scholl told the Guardian. And certainly Van Gaal: The Early Years looks like a rare talent at work. The Ajax team he led to three league titles, the Uefa Cup and Champions League in the mid-1990s is one of the great untempered footballing joys of the modern age, a team of brilliant players – Marc Overmars, Dennis Bergkamp, Frank and Ronald de Boer, Edgar Davids, Clarence Seedorf – managed according to a seductive total football template. Van Gaal's Ajax became champions of Europe with an average age of 23, beating a dominant Milan in the final with a goal from the 18-year-old substitute Patrick Kluivert. Had he achieved nothing else afterwards, this was a mini-era to set his name in stone.

The subsequent years have been good, if not as luminous. It is worth noting that Van Gaal, widely proclaimed serial winner, has won two league titles and the German Cup in the past 15 rather staccato years, taking in his disorientating, aborted succession to Ferguson in 2002, a difficult second spell at Barcelona and periods with the Dutch national team. His outstanding achievement in that time was another superb standalone league title with AZ Alkmaar, in a year when Van Gaal might have left the club but ended up instead recalibrating his team dramatically and drawing from his players a season of sublime total football overachievement.

Three spells at Europe's established financial giants – Bayern and Barça twice – have ended less well. Despite winning two Spanish titles, Van Gaal was whistled away from the Camp Nou and sacked with Barcelona three points above the relegation zone, a manager perhaps too interested in promoting the theory and practice of Van Gaal than submitting wholesale to the Catalan way. This despite the fact that beneath the antipathy Van Gaal was stoking the Barça academy production line and honing that possession-based style.

This is something that could work in United's favour. Van Gaal – who lost up to £4m in the Bernard Madoff scandal in 2009 – remains a hungry-looking managerial genius, a man who clearly feels he has unfinished business, another dynasty in him.

This is where the Dutchman starts to distinguish himself most favourably from his immediate successor. With United right now it isn't just about trophies won or clubs managed, but methods, development and attitude. This is a club still in the process of a traumatic succession. Van Gaal has the aura, but more than that the philosophy, the clear and unarguable structures to make a productive break with the old ways. We're not talking Steve Round, Jimmy Lumsden and Phil Neville here. Van Gaal is an enduring intellectual aristocrat of the European game, with a strong personal connection to a distinct footballing philosophy, Ajax's triumphant total football of the 1970s and his own bespoke 90s era. In this light Van Gaal again starts to look less like a stopgap or a three-season stabilising force and more like a more wide-ranging answer to United's current need for a clear-out, a bolt-on set of methods, an answer to the basic question of how this team wants to play.

The players will need to adapt. Van Gaal fell out with Rivaldo at Barcelona and traumatised Franck Ribéry for a while at Bayern ("When the coach always speaks badly about you, when he keeps on putting you down, then it is tough," he said at the time). But hindsight suggests this ruthlessness is what United needed most after Ferguson, and what Van Gaal would have brought as standard. Not that Van Gaal is unable to manage transition and continuity where necessary: witness his well-managed succession from Robson at Barcelona, where Robson was retained as a high-end roving scout and Mourinho promoted from translator to coach because Van Gaal recognised him as an asset.

Plus, Van Gaal is a master of player development and fearless in his promotion of talented youth. Historically, this is the United way. Van Gaal is a manager who puts down foundations. In his time at Bayern they won a league title and reached a Champions League final, but just as significantly Van Gaal installed some key components of their subsequent successes. He signed Arjen Robben, converted Bastian Schweinsteiger into a central midfielder and helped ease David Alaba, Thomas Müller, Holger Badstuber, Toni Kroos and Mats Hummels into the first team. At Ajax, he revamped the academy and helped a generation of players to bloom. At Barcelona, he gave Andrés Iniesta, Xavi, Carles Puyol and Lionel Messi a concerted start.

This is the real point of distinction with his predecessor – not so much the trophies won as the sense of a coherent, large-scale, fearless big-club methodology. If he is given time that is. Van Gaal has traditionally been a slow starter. He makes no apology for this: he is instilling a method and there will naturally be a spasm of accommodation. At Bayern and Alkmaar it took a while before his teams began to thrum with trophy-winning good health.

Plus, there is the issue of tactics. Van Gaal is perhaps best cast as mid-point between Mourinho and Pep Guardiola, a genuine Ajax aficionado with a fetish also for hands-on defensive drilling. His teams attack, but they do so with a due sense of process.

For Van Gaal, the midfield distributor has often been a key player. At Barcelona he had first Guardiola and then Xavi and it is here he is likely to strengthen at United, barring an unexpected passion for Michael Carrick. Somewhere in between Kroos and Kevin Strootman the answer may lie. Beyond that No10/attacking midfield is another Van Gaal hot spot from his Ajax days. Good news perhaps for Wayne Rooney, Juan Mata and Shinji Kagawa, albeit the new manager has tended to favour fast, mobile players who can beat a man close to goal (hence the importance of Robben – still – at Bayern). Marco Reus, should he become available, would be an excellent fit.

This sense of a well-grooved elite level tactical model is again where Van Gaal stands apart from Moyes, albeit the sheer density of his blueprint may present a problem in itself. As outlined in a tactical presentation during his time at Barcelona. Van Gaal breaks football down into four phases, from non-possession, to about to gain possession, to actual possession and all the way back to playing without possession again. Within this, possession itself is not one but four things, a finely nuanced process that runs from slow-build possession, to pre-chance creation possession, to chance creation possession and, finally, to either scoring or failing to score a goal. Van Gaal's formations divide the pitch not into straight lines but interlocking triangles. At Alkmaar, he adopted an innovative 4-4-2 formation, described in these pages as "Total Football 2.0".

There is a lot of theory here, a lot of posturing, a lot of academic control freakery. "His thing is working on the pitch," Scholl said. "That's how the players learn. You know by yourself that if you learn from somebody you are curious, you want to learn more." Some do and some don't. How well experienced English footballers – not to mention the class of '92 coaching core – take to being forcefully re-educated along these lines will be fascinating to watch.

Similarly, the overlap between Van Gaal's fierce – and at times very funny – intellectual snobbery promises to be a gripping subplot. This is a man who has fallen out spectacularly with one overbearing in-house father figure in Uli Hoeness. Who remains enduringly combustible in all his professional relations. And who – promisingly – has been known to explode with anger at being asked "stupid questions" by journalists. Welcome to England, Louis. It promises to be anything but dull.