British regulators on Friday gave final approval to Microsoft’s $69 billion acquisition of the video game publisher Activision Blizzard, the last major obstacle for a deal that at one point seemed to be falling apart because of government objections on both sides of the Atlantic.

Britain’s antitrust agency, the Competition and Markets Authority, said it signed off on the deal after Microsoft agreed to license to a rival a part of Activision’s business associated with so-called cloud gaming, a small but promising new area for the industry. The C.M.A. was the last regulator that needed to approve the deal before it could be finalized.

The approval is a major victory for Microsoft, which has spent nearly two years fighting objections in the United States and Britain. In July, the company won a court case against the Federal Trade Commission, which had tried to block the deal. And after British authorities said they would block the acquisition in April, Microsoft was able to convince them to reverse course, a rare occurrence for the C.M.A.

Microsoft and Activision are expected to complete the transaction in the coming days.

“The C.M.A. is resolute in its determination to prevent mergers that harm competition and deliver bad outcomes for consumers and businesses,” said Sarah Cardell, chief executive of the antitrust agency. “We delivered a clear message to Microsoft that the deal would be blocked unless they comprehensively addressed our concerns and stuck to our guns on that.”