LOS ANGELES — Personal computers at home and in the office will soon be displaced by the tablet as the primary computing device, according to a new report from Forrester Research.

Tablet sales are expected to grow sharply from 56 million in 2011 to 375 million in 2016, according to the report. Given that most users keep their tablets for three years, there will probably be 760 million tablets in use globally by 2016, said Frank Gillette of Forrester’s business technology futures team.

As a result, the tablet will replace the PC as the user’s digital hub, connecting devices such as smartphones, desktop computers and content stored in cloud services — remote servers that can be accessed from anywhere with an Internet connection.

Eventually these burgeoning cloud services such as Dropbox, SugarSync and Box will dictate what devices consumers will use, according to the report.

As for market leaders, Apple Inc. is expected to maintain its dominance, even as its market share erodes amid increased competition. Google Inc. is expected to lose some market share because of a fragmented market and competition from tablets running Microsoft Corp.’s Windows 8 software.

Although Microsoft is playing catch-up behind Apple and Google in terms of available apps, Gillette said that “once rolling, however, we expect Microsoft will be a significant player.”

Ultimately, in the next decade, PCs will be redefined, the report said. “PC no longer will mean personal computers — instead it will be the full spectrum of personal computing, from personal cloud services to the broad range of personal technology used for work, including tablets, smartphones and frames,” Gillette wrote.