Now the hard part begins.

After a six-months-long search, Microsoft has handed responsibility for its future to Satya Nadella, who replaces Steve Ballmer and becomes only the third chief executive in the company's nearly four-decade-long history.

Founder Bill Gates, meanwhile, will move over as a "technology advisor," suggesting a more active role in the development of Microsoft product. John Thompson will take over as chairman.

"Satya is a proven leader with hard-core engineering skills, business vision, and the ability to bring people together," Gates said in a prepared statement. "His vision for how technology will be used and experienced around the world is exactly what Microsoft needs as the company enters its next chapter of expanded product innovation and growth."

In choosing Nadella, the executive vice president of Microsoft's Cloud and Enterprise group, Microsoft has turned to a highly accomplished executive in the mold of its co-founder Gates, who reportedly held out for a candidate with sufficient technical gravitas to inspire -- and if need be, change -- Microsoft's engineer-driven corporate culture. It also confounded the early handicapping in the CEO vetting process that the board needed to land an outside candidate to shake things up.

At the still relatively young age of 46, Nadella oversaw one of Microsoft's fastest-growing divisions -- the Cloud and Enterprise Group -- which accounted for $20.3 billion in revenue and $8.2 billion in operating income during the company's last fiscal year.

Outsiders and colleagues credit Nadella with helping to move Microsoft's server and tools group to a faster, more agile development model - so they are no longer innovating on long, 18-month release cycles. At the same time, he's been a key player in forcing a shift in the business focus to the cloud and software-as-a-service. Brad Silverberg, who co-founded the venture investment firm Ignition Partners after a long and successful career at Microsoft, noted that Nadella had done "a remarkable job" moving Microsoft to the cloud, where its Azure service is now a strong rival to Amazon Web Services. (You can read Silverberg's guest column on the Nadella appointment here.

James Martin/CNET

The new boss walks into a job where there's lots to celebrate but also lots to worry about for a company still seeking to figure out its place in a post-PC world. Perhaps the most pressing question facing Nadella will be whether it's worth keeping Microsoft's different pieces together or recasting the company with fewer lines of business. But analysts familiar with Nadella say his track record is a promising harbinger.

"Satya Nadella is a tough, number-driven leader," said Forrester's Ted Schadler. "He is a visionary, has passion for change, is making it happen, and knows what it takes to drive change in the unique Microsoft culture. An outsider would have a hard time accomplishing this coming in fresh. And time is of the essence."

There's a school of thought that suggests Microsoft is simply too big to compete with slicker, faster-moving companies born in the Internet era. If Nadella buys into that worldview, he may decide to sell off the Xbox and Bing businesses as Nomura Equity Research's Rick Sherlund has argued. Earlier this year, Sherlund sketched out a scenario in which Microsoft sells Bing either to Facebook or Yahoo while shopping the Xbox business around to a consumer electronics company where it would make a better fit.

That's the Wall Street view, at least. Nothing new there as the Street has been down on Bing for quite some time. The online services division, the corporate organization where Bing resides, lost $1.3 billion last year. The year before, it lost $8.1 billion. But with Microsoft integrating its search technology into nearly all of its software and hardware as a service, Nadella may decide, like Ballmer, that there's a nice strategic fit here. Also, there's a good argument for keeping Xbox: It's a growth area with terrific upside. So why jettison the business just as it's realizing its potential?

Obviously, Nadella will have to sort through competing visions of the future, but he doesn't need to to rush his decision. The good news is that there's nothing immediately troubling the company's bread-and-butter business of Windows and Office, and that's what pays the bills. Also, Windows Azure, the company's cloud platform, rates as an unqualified success, now pulling in more than a billion dollars each quarter. And given Nadella's familiarity with Microsoft's enterprise business, the engine behind its earnings momentum, investors can remain sanguine that the new boss won't screw around with a winning formula.

As the baton officially gets passed from Ballmer, who announced last August that he intended to leave the job within the following 12 months, the countdown is getting under way. Nadella still has to work out where to point Microsoft in a world increasingly dominated by tablets and software that resides on the cloud. PC sales continued their decline in the fourth quarter of 2013 -- and that's not going to reverse, a troubling harbinger for the company's cash cow Windows monopoly.

Read more on ZDNet: Steve Ballmer, the exit interview

Another challenge: Can Microsoft foster the sort of app ecosystem that Google and Apple have so successfully created? The bold decision to buy Nokia's device business opens a more direct front of competition against its two chief rivals. But jumping into the phone hardware business, a market where Microsoft has had uneven success, presents the new CEO with a fait accompli. Now it's up to Nadella to figure out how to make this latest division work with the rest of his newly inherited tech conglomerate.

Big questions and no easy answers.