The European Commission, the bloc's powerful anti-trust authority, said the approval was "conditional on full compliance with the commitments offered by Microsoft."
The European Commission said that if Microsoft lives up to its promises, it will allow gamers to stream Activision's titles on any cloud gaming streaming services operating in Europe.
"The European Commission has required Microsoft to license popular Activision Blizzard games automatically to competing cloud gaming services," Microsoft vice chair Brad Smith said.
"This will apply globally and will empower millions of consumers worldwide to play these games on any device they choose."
But, unless Microsoft wins an appeal against the block by Britain's Competition and Markets Authority (CMA) last month, experts say it will be game over for the bid.
The CMA blocked the bid over concerns it could kill competition in the fast-growing cloud gaming market, and lead to less choice for British gamers in the future.
"If Microsoft does not win the appeal in the CAT, it cannot proceed with the acquisition even if the European Commission now approves it," said Anne Witt, a professor of anti-trust law at EDHEC business school in France.
"Unless, of course, Microsoft decides to leave the U.K. market. But that seems unlikely," she told AFP earlier this year.
The deal is also under threat in the U.S. giant's homeland, where last year the Federal Trade Commission launched a legal action to block it, one of Washington's biggest ever interventions to stop tech industry consolidation.
Xbox-owner Microsoft launched its gigantic bid for Activision Blizzard early last year to create the world's third biggest gaming firm by revenue after China's Tencent and Japan's PlayStation maker Sony, provoking antitrust concerns.
Activision Blizzard's hit titles also include "Candy Crush" and "World of Warcraft." If it goes ahead, it will be the biggest deal ever in gaming.