Indian-born Mr Nadella is currently Microsoft’s head of Cloud and Enterprise, which builds and runs the firm’s computing platforms and developer tools.
He takes over from Steve Ballmer who announced plans to step down last year.
Company founder Bill Gates said there was “no better person to lead Microsoft”.
Mr Gates is stepping down as chairman, it was also announced, but will take up a new role as technology adviser and will also retain a seat on Microsoft’s board.
Microsoft’s lead independent director John Thompson will take over as chairman.
‘Proven leader’
“Microsoft is one of those rare companies to have truly revolutionised the world through technology, and I couldn’t be more honoured to have been chosen to lead the company,” said Mr Nadella.
Mr Nadella, 46, is Microsoft’s third chief executive. The Hyderabad-born executive joined the company in 1992 and has degrees in electronics, computer science and business administration.
He previously led its server and tools business before being put in charge of the unit that built Microsoft’s Cloud OS service, which powers products such as Bing, Skype and Xbox Live.
“During this time of transformation, there is no better person to lead Microsoft than Satya Nadella,” said Mr Gates.
“Satya is a proven leader with hard-core engineering skills, business vision and the ability to bring people together. 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.”
The appointment ends months of speculation over who would succeed Mr Ballmer, who announced his intention to stand down in August last year.
At one stage incoming chairman John Thompson said more than 100 possible candidates had been identified.
Rumoured to be among them were the boss of car giant Ford, Alan Mulally, and Nokia chief executive Stephen Elop.
Investors have been calling for new leadership at the Microsoft, saying it needs a significant shakeup in order to become more innovative and profitable.
Some critics have questioned whether Mr Nadella is the right man for the job. He has no experience of running a company, let alone one as big as Microsoft.
Microsoft shares rose following the announcement. They were up 0.7% after an hour of trading.
-BBC
