Facebook Inc. (Nasdaq: FB) has won approval from the U.S. Federal Trade Commission for its planned acquisition of Instagram Inc., a photo-sharing service popular on mobile devices.

The FTC closed its antitrust review of the transaction with a unanimous 5-0 vote of the commissioners, allowing the purchase to proceed, the agency said Wednesday in a statement on its website.

“We are pleased that the Federal Trade Commission has cleared the transaction after its careful and thorough review,” the Menlo Park, California-based company said in an e-mailed statement.

Facebook, under investor scrutiny for its performance in the mobile sector, is buying Instagram to bolster its presence on wireless devices, where it needs to capture more attention from users and boost advertising dollars as it competes with rival Google Inc. (Nasdaq: GOOG). The company said earlier this year that sales growth is failing to keep pace with the increasing number of users as more members access the service from tablets and smartphones.

Facebook in April offered to buy the closely held photo- sharing site for $300 million in cash plus about 23 million shares of common stock, a deal valued at almost $750 million based on yesterday’s closing price. Instagram is a photo application popular on smartphones, such as the Apple Inc. iPhone, allowing users to quickly take pictures, modify them and share them with friends.

The company said last month the acquisition is expected to close in 2012.

The company still faces a fairness hearing by the California Department of Corporations on Aug. 29 in San Francisco to consider an application by Facebook to issues securities in connection with the proposed purchase of San Francisco-based Instagram.