This comes just one day after the Delaware Supreme Court reversed an earlier judicial decision that halted the transaction.
Activision, the world's biggest video game publisher, acquired 429 million shares from Vivendi for about $5.83 billion in cash, or $13.60 a share. Activision Chief Executive Bobby Kotick, Co-Chairman Brian Kelly and their investment vehicle bought about 172 million shares from Vivendi at a cost of $2.34 billion.
That leaves Paris-based Vivendi, which has been looking to shed assets, in possession of 12% of Activision, the firm behind the popular "Call of Duty" franchise.
"With the completion of this transaction we open a new chapter in the history of Activision Blizzard," Kotick said in a statement. "Our shareholders and debt holders will have the benefit of an energized, invested, deeply committed management team focused on generating long-term, superior returns and effectively managing our capital structure."
On Thursday, the Delaware high court overturned a Delaware Chancery Court decision that preliminarily enjoined the transaction after Douglas Hayes, an Activision shareholder, sued the company, Vivendi and the investor group.
In the lawsuit, Hayes contended the deal should have been put to Activision's shareholders for a majority vote. The Delaware high court's chief justice Myron T. Steele said the transaction did not require the approval of non-Vivendi shareholders.