Delta Air Lines Inc. won U.S. Justice Department approval of its proposed equity investment in Richard Branson’s Virgin Atlantic Airways Ltd. and of the carriers’ related trans-Atlantic joint venture.

The department’s antitrust division announced today that it had closed its investigation into the deal, allowing it to proceed. European regulators have also signed off on the transaction.

“The facts and circumstances did not warrant further investigation or action,” the Justice Department said in an e-mailed statement.

Delta, based in Atlanta, agreed on Dec. 11 to buy a 49 percent stake in the U.K. carrier for $360 million to boost its share of the trans-Atlantic travel market. The agreement included a joint venture on 31 daily round-trip flights between North America and the U.K. Virgin Group retains a 51 percent stake.

Delta also won European Union approval for the transaction, according to an e-mailed statement from EU regulators today.

“The division and the European Commission cooperated closely throughout the course of their respective investigations, with frequent contact between the agencies,” the Justice Department said. “This cooperation, facilitated by the parties, made for a more efficient review process.”

Transportation Department

Delta and Virgin Atlantic also have filed an application with the U.S. Transportation Department seeking antitrust immunity for their joint venture, according to the Justice Department statement. The antitrust division said it would consult, as appropriate, with that agency as it reviews the immunity request.

“Delta is pleased with today’s decisions by the DOJ and European Commission approving full merger clearance for the proposed transaction,” Anthony Black, a company spokesman, said in an e-mail.

The U.S. carrier’s 10 daily nonstop flights to the U.K. would be added to the 21 that Crawley, England-based Virgin Atlantic plans to operate under its summer 2013 schedule.

While the Virgin Atlantic brand will remain and founder Branson will retain control, the deal marks the end of a go-it-alone strategy for the airline the 62-year-old U.K. billionaire established almost three decades ago.

25% Share

Delta’s current share of U.S.-U.K. flying is about 8 percent, and the venture would have 25 percent, Delta Chief Executive Officer Richard Anderson said on a December conference call. British Airways and American Airlines, which have an immunized joint venture, control about 60 percent of the market, Anderson said.

By linking itself with Virgin, Delta is targeting North Atlantic flights that generate roughly one-quarter of all global revenue from first- and business-class fares, more than twice as much as second-place trans-Pacific routes, according to the International Air Transport Association.