Deutsche Telekom AG’s proposal to combine its T-Mobile USA unit with smaller MetroPCS Communications Inc. won approval from U.S. competition and telecommunications authorities.

Allowing the fourth- and fifth-largest U.S. wireless carriers to combine will benefit American consumers as the mobile market continues to strengthen, Federal Communications Commission Chairman Julius Genachowski said in an e-mailed statement today. Benefits include more high-speed wireless service, the agency said in an order.

The combination is unlikely to harm consumers, and may help T-Mobile become a stronger competitor, the Justice Department said in an e-mailed news release announcing it closed its investigation into the deal.

David Henderson and Jim Mathias, spokesmen for Bellevue, Washington-based T-Mobile and Richardson, Texas-based MetroPCS, didn’t immediately return voicemail and e-mail messages seeking comment.

The deal aims to reinvigorate T-Mobile, a target of a failed purchase attempt by second-largest U.S. wireless carrier AT&T Inc. in 2011. T-Mobile will take on subscribers and capacity from MetroPCS to compete with AT&T, market leader Verizon Wireless and Sprint Nextel Corp., the third-largest U.S. provider.

Deutsche Telekom, Germany’s largest telephone company, on Oct. 3 announced the deal that will leave the Bonn-based company with 74 percent of the new business after paying MetroPCS shareholders $1.5 billion in cash.

MetroPCS dropped 18 cents at 2:48 p.m. New York time to $10.32, 29 percent below its October high as news of the deal broke. Deutsche Telekom’s American depositary receipts, each representing one share, dropped 8 cents to $10.85.

Paulson & Co., the biggest investor in MetroPCS, has said it wants to block the deal. The combined company would hold too much debt, John Paulson, founder and majority owner, said in a Feb. 28 letter to the MetroPCS and Deutsche Telekom boards.