"It all ends," says the poster slogan. A potentially grim statement of the obvious, of course, yet the Potter saga could hardly have ended on a better note. With one miraculous flourish of its wand, the franchise has restored the essential magic to the Potter legend – which had been starting to sag and drift in recent movies – zapping us all with a cracking final chapter, which looks far superior to CS Lewis's The Last Battle or JRR Tolkien's The Return of the King. It's dramatically satisfying, spectacular and terrifically exciting, easily justifying the decision to split the last book into two.

Here is where the Harry Potter series gets its groove back, with a final confrontation between Voldemort (Ralph Fiennes) and our young hero, and with the sensational revelation of Harry's destiny, which Dumbledore had been keeping secret from him. When stout-hearted young Neville Longbottom (a scene-stealer from Matthew Lewis) steps forward to denounce the dark lord in the final courtyard scene, I was on the edge of my seat. And when, in that final "coda", the middle-age Harry Potter gently hugs his little boy before sending him off for his first term at Hogwarts – well, what can I say? I think I must have had something in my eye.

The colossal achievement of this series really is something to wonder at. The Harry Potter movies showed us their characters growing older in real time: unlike Just William or Bart Simpson, Daniel Radcliffe's Harry was going to grow up like a normal person and never before has any film – or any book – brought home to me how terribly brief childhood is. The Potter movies weren't just an adaptation of a series of books, but a living, evolving collaborative phenomenon between page and screen. The first movie, Philosopher's Stone, came out in 2001, when JK Rowling was working on the fifth book, Order of the Phoenix, and when no one – perhaps not even the author herself – knew precisely how it was going to end. The movies developed just behind the books, and it's surely impossible to read them without being influenced by the films. This is most true for Robbie Coltrane's endlessly lovable, definitive performance as Hagrid.

In this final episode, Harry (Radcliffe), Hermione (Emma Watson) and Ron (Rupert Grint) continue their battle to find and destroy the "horcruxes" that the sinister Voldemort needs so he can stay alive for all eternity: these are objects in which the fragments of souls are trapped and whose vital, spiritual force Voldemort, that hateful parasite, can siphon off for his own ends. Harry and his friends track down these horcruxes, but the last one is a puzzle. As the forces of good assemble at Hogwarts for the final showdown with Voldemort and his hordes, Harry knows only that the most vital horcrux is actually in the castle, very close at hand.

There are some superb set-piece scenes – and now the plot has so much more zing, these scenes have a power that comparable moments in earlier movies did not have. When Harry, Ron and Hermione insinuate themselves into Gringotts Bank to steal the sword of Gryffindor, the effect is bizarre, surreal and macabre: drawing on the influence of Lewis Carroll and Terry Gilliam. It is a great moment when Severus Snape, played with magnificently adenoidal disdain by Alan Rickman, is attacked by Voldemort's snake Nagini, and we witness this only from behind a frosted glass screen – a nice touch from director David Yates. London-dwelling Potter fans will, as before, be intrigued to see how the ornate St Pancras railway station is used to represent King's Cross, from where the Hogwarts train traditionally departs. Millions of tourists are undoubtedly convinced that this building is, in fact, King's Cross. It may be forced simply to change its name.

We get passionate, but somehow touchingly innocent screen kisses between Harry and Ginny (Bonnie Wright) and, of course, between Ron and Hermione. In the midst of the battle, Neville declares that he is going to find Luna (Evanna Lynch) for a snog: "I'm mad about her! About time I told her, since we're both probably going to be dead by dawn!" But these love stories are always subordinate to the all-important battle between good and evil.

The crucial moment of the film is where, I admit, I have a quibble: it is gripping and even moving when Harry realises what his destiny is, and sets out to fulfil it. Yet the exact rationale for his ultimate survival may be a little obscure, and perhaps even Potter-diehards may suspect that in the film there is a touch of having your cake and eating it. Well, no matter. This is such an entertaining, beguiling, charming and exciting picture. It reminded me of the thrill I felt on seeing the very first one, 10 years ago. And Radcliffe's Harry Potter has emerged as a complex, confident, vulnerable, courageous character – most likable, sadly, at the point where we must leave him for ever. Wait. I've got that darn thing in my eye again ...