The green light is a success for Drahi, who made his fortune through debt-fuelled acquisitions in the cable and telecoms sectors on both sides of the Atlantic.
Altice Europe's shareholders met in Amsterdam on Thursday to vote on a series of items, including Drahi's bid.
The proposal initially drew heavy criticism from several minority shareholders, prompting the Franco-Israeli tycoon to raise his offer per share to 5.35 euros from 4.11 euros.
The hike brought the group's equity valuation to 6.4 billion euros ($7.85 billion). At end of September, Altice Europe's net debt amounted to about 29 billion euros.
The bid, which runs until Jan. 21, comes after years of investor scrutiny over Altice Europe's high debt levels, which have weighed on its share price.
The company has recently chipped away at that burden and has increased subscriber numbers in France, where it makes more than half of its revenues.
"(The resolutions) were all passed," said David Tomic of the VEB, an organization that represents shareholders' rights in the Netherlands and has been critical of the disproportionate power given to Drahi under the company's share structure.
"I don't have the exact numbers, but they will be published on the company website in the course of today."
($1 = 0.8151 euros)
(Reporting by Toby Sterling; Writing by Mathieu Rosemain; Editing by Jason Neely and Jan Harvey)
By Toby Sterling