LOS ANGELES — As longtime Microsoft insider Satya Nadella takes the company’s helm, he is declaring a new focus on a “mobile-first, cloud-first world.” So far, he only has the latter half of the formula figured out.

Microsoft and its new CEO are trying to catch rivals such as Apple, Google and Amazon, which are each building their own thriving ecosystems for mobile devices. At the same time, the company wants to expand its burgeoning business as a provider of software and services over the Internet.

Nadella, head of Microsoft’s cloud computing business, was named Tuesday to be Steve Ballmer’s immediate replacement. He is only the third chief executive in Microsoft’s 38-year history.

The 22-year Microsoft veteran has enlisted the help of company founder and first CEO Bill Gates, who is leaving his role as chairman to serve as an adviser at Nadella’s request. Gates will spend a third of his time working on products and technology.

Nadella, 46, led the company’s growing cloud computing unit, in which customers pay Microsoft to house data and run applications on distant servers connected to the Internet. Those services are a departure from Microsoft’s traditional business of making software for installation directly onto personal computers.

One of Nadella’s first tasks as CEO will be to complete Microsoft Inc.’s $7.3 billion purchase of Nokia’s phone business and patent rights — part of a plan to boost Windows Phone software in a market dominated by iPhones and Android devices.