NEW YORK – Microsoft, more than any other traditional software company, has swiftly and profitably made the shift to delivering software as an internet service.

The technology giant reinforced how well it has made that transition on Thursday, when it reported strong gains in both profits and sales in its fiscal third quarter, led by the rapid growth of its cloud software business.

The company’s net income rose 35 percent from a year earlier, to $7.4 billion. Revenue rose 16 percent to $26.8 billion in the quarter, exceeding the Wall Street consensus forecast of nearly $25.8 billion.

Microsoft’s earnings per share increased 36 percent to 95 cents a share, well above the analysts’ average estimate of 85 cents a share, compiled by Thomson Reuters.

Since Satya Nadella became chief executive in 2014, the cloud portion of Microsoft’s revenue has soared from 3 percent to more than 21 percent this year, according to estimates by Credit Suisse.

In an interview, Amy Hood, the company’s chief financial officer, described the quarter as a “very strong” performance, “driven by the ongoing demand for our cloud services.”

Azure, the company’s unit supplying cloud-based computer processing and storage, grew by 93 percent compared with the same quarter a year ago. Microsoft is now a strong No. 2, behind Amazon, in this market for the foundation layer of cloud technology. Microsoft finished 2017 with 13 percent of the cloud infrastructure services market, according to Synergy Research Group, a gain of 3 percentage points during the year.

Amazon held 34 percent of that market, up half a percentage point. Corporate customers, analysts say, often want more than one cloud supplier as they move to cloud technology — a trend that helps Microsoft.

Microsoft’s broader commercial cloud division, which includes Azure and customer and operations management software for corporations, grew by 58 percent.

The cloud transition is changing the company’s business model to one with a rising share of steady, recurring revenue from cloud subscriptions rather than traditional software sales. Including contributions from cloud-based versions of its Office productivity software and online gaming subscriptions, recurring revenue streams now account for about 30 percent of Microsoft’s sales, said Michael Nemeroff, an analyst at Credit Suisse.

That share, Nemeroff estimates, could reach more than 50 percent in four years.

The successful shift to the cloud and the subscription sales model has pleased investors. Microsoft’s shares have climbed roughly 40 percent in the past year. The company’s share price slipped by 1 percent in after-hours trading Thursday, after gaining 2 percent during the regular session.

Not long ago, Microsoft was considered a faded power among big tech companies. Today its stock market value, while behind Apple, is neck and neck with Amazon’s and slightly ahead of Google’s.

The personal computer software business, once Microsoft’s mainstay, has been eroding for years, as people spend more of their computing time on smartphones. But personal computer shipments have held steady recently as businesses replace old PCs with new ones that use the latest Microsoft operating system, Windows 10.

The Windows PC operating system business is in a division Microsoft calls “more personal computing,” which grew by 13 percent. And Windows sales directly to PC makers grew by 4 percent.