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.”

The acquisition is the largest consumer technology deal since AOL bought Time Warner two decades ago, and it will combine Microsoft’s Xbox business with the world’s largest game publisher. Activision publishes titles such as “Call of Duty,” “Candy Crush,” and “World of Warcraft.”

“We have now crossed the final regulatory hurdle to close this acquisition, which we believe will benefit players and the gaming industry worldwide,” Brad Smith, the vice chair and president of Microsoft, said in a statement.

Bobby Kotick, the chief executive of Activision Blizzard, said he and his colleagues “look forward to becoming part of the Xbox team.”

Microsoft’s ability to push past the regulatory concerns shows the limits of government efforts to crimp the power of the world’s largest tech companies. First announced in January 2022, the acquisition was seen as a test of whether regulators could block a tech megamerger amid concerns about the industry’s growing economic might and societal influence.

Microsoft made a number of concessions to win approval. The company said it would not block Activision titles from being available for rival consoles such as Sony’s PlayStation.

To assuage concerns from British authorities, the company agreed to transfer the cloud streaming licensing rights for all current and new Activision Blizzard games to Ubisoft Entertainment, a rival game publisher in France.

Cloud gaming is still a very small market, but has the potential to be a major area of growth for the industry because the technology allows people to stream games on phones, tablets and other devices, diminishing the need for traditional consoles.

The arrangement is seen as preventing Microsoft from using Activision titles to give its cloud-gaming service an advantage over rival offerings. The structure will last for 15 years and apply to all markets except for the European Union, which approved the deal without the cloud gaming concession.