AT&T Inc., seeking to add wireless-network capacity for services such as online video, won approval from regulators yesterday to buy airwaves from Providence-based Aloha Partners LP for $2.5 billion.

AT&T’s purchase of the airwaves, covering 196 million potential customers in 281 markets, will “serve the public interest” and is unlikely to harm competition, the Federal Communications Commission said in a 4-to-1 decision released yesterday.

The spectrum, which reaches 72 of the top 100 U.S. markets, will let AT&T add more mobile Internet and messaging services as revenue from home-phone customers declines. The airwaves are in the same spectrum band as those AT&T is bidding for in a FCC auction that began Jan. 24.

AT&T, the biggest U.S. telephone company, announced plans to buy Aloha on Oct. 9. San Antonio-based AT&T said at the time that the purchase would close in six to nine months.

Aloha, a privately held company that lists its headquarters as 4 Richmond Square, says it is the largest holder of 700-megahertz licenses in the country and has built its portfolio of licenses over the past six years. Most of it was bought through government auctions in 2001 and 2003; the rest was bought from other license holders. The sale to AT&T includes all the licenses Aloha holds.

Included in the AT&T deal are the 32 broadcast spectrum licenses in 17 U.S. markets that Aloha acquired from Providence-based LIN TV for $32.5 million in cash in September.

Except for two limited market trials, Aloha never used the airwaves to build a wireless network.

Aloha was founded by Charles Townsend and Amos Hostetter, who made their fortunes in the wireless and cable business in the 1990s, according to the Associated Press.

Townsend, of Barrington, is the former president and chief operating officer of The Providence Journal Co.’s former cable television company. (The newspaper no longer owns cable television systems.)

The sale can’t be completed until AT&T reimburses the government for discounts Aloha received for the airwaves it bought at FCC auctions. While Aloha qualified for the 35-percent discounts, AT&T isn’t eligible because they are intended for small businesses, the FCC said yesterday.

Commissioner Michael Copps, one of two Democrats on the five-member FCC, cast the lone dissenting vote. The agency’s decision was “hasty” and “seems destined to reduce competition and diversity,” Copps said in a statement on the FCC’s Web site. The FCC said it didn’t receive any comments from the public opposing the deal.

In the statement, Copps said the FCC order constitutes “a rush to judgment” on the part of the FCC using a method of analysis that includes “sloppy math and inaccurate assumptions.” He said the transfer “seems destined to reduce competition and diversity in the wireless marketplace.”

AT&T told the FCC the transaction would allow the company to “meet the growing demand for spectrum-intensive wireless data and content services and to provide these services more cost effectively.”

AT&T fell 12 cents to $38.16 in New York Stock Exchange composite trading. The stock has fallen 8.2 percent this year.