The company also said Bill Gates would step aside as chairman of the board but would remain a technology adviser to the company. John Thompson, who has been the lead independent director, will become chairman.
Nadella's appointment ends a longer-than-expected search for a new leader after Steve Ballmer announced his intention to retire in August.
Nadella is only the third CEO in Microsoft's 39-year history, following co-founder Bill Gates and Ballmer.
"This is a critical time for the industry and for Microsoft."
The company took to Twitter to introduce its choice as CEO to the world.
In an email to Microsoft staff, Nadella acknowledged there was work to be done.
"While we have seen great success, we are hungry to do more. Our industry does not respect tradition — it only respects innovation. This is a critical time for the industry and for Microsoft," he said.
Nadella, most recently, head of Microsoft's cloud and enterprise business, has held various executive positions since joining the company in 1992. He previously led Microsoft's server and tools business.
Before Microsoft, the Indian-born executive worked at Sun Microsystems.
The famously ebullient Ballmer -- who joined Microsoft in 1980 as the company's first business manager and rose quickly through the ranks -- leaves the company after 13 difficult years as CEO. The company was once the most valuable in the world, but Microsoft has lost more than half of its market value over the past decade.