Weiner, 47, joined the union in 1988 and had been its chief negotiator.
Players voted overwhelmingly in October to approve Weiner and the union's executive board unanimously confirmed his appointment Wednesday in Scottsdale, Ariz.
Fehr, who had held the post since December 1983, wanted Weiner to succeed him.
Weiner must deal with a shorter post-season, the banned human-growth hormone and a possible salary cap for team payrolls.
"We are confident the future of our union is in good hands with Michael at the helm," said Arizona first baseman Tony Clark, the union's player representative. "We all owe Don a tremendous debt of gratitude. I want to thank him for all he accomplished during his tenure."