The $220 million deal, which was announced in November, was approved on condition the companies sell Craft Brew Alliance's Kona brand beer.
The Portland-based CBA's other brands include Appalachian Mountain Brewery, Cisco Brewers, Redhook Brewery and Widmer Brothers Brewing.
Anheuser-Busch owned 31.2% of CBA before the deal was announced, and also distributed many of CBA's brands.
"CBA's diverse portfolio of national lifestyle brands and award-winning regional breweries are an excellent complement to our family of craft partners," said Marcelo Michaelis, president of ABI's Brewers Collective business unit.
The companies said in a release that closing was expected "in the coming weeks."
By Diane Bartz