The sale, which includes UKís Meantime brewery and Miller Brands UK, is aimed at easing competition and other regulatory concerns occasioned by AB InBevís £70 billion acquisition of SAB Miller, announced towards the end of last year.
The deal is conditional on the completion of the AB InBev SAB Miller merger.
It represents Asahiís largest acquisition yet, and is the biggest transaction in the competitive Japanese drinks market since since Suntoryís 2014 acquisition of Beam Inc for £11 billion.
Japanís drinkers are increasingly turning away from beer, and domestic sales at Japanís five leading brewers have declined every year in the last decade, the†Nikkei Asian Review reports.
Asahi fended off competition for the brands from a number of rivals, including Thailandís largest brewery, Thai Bev.
Former Diageo chief executive, Paul Walsh, also explored a bid in partnership with private equity firm, TPG Capital.
The £1.8 billion bid values the brands at some 14 times earnings, the Financial Times reports.
ďAsahi aims to expand its growth platform in Europe and become a global player with a distinct position,Ē the group said in a statement.
In related news, Heineken the worldís third largest brewer, reported 2015 profits of £1.5 billion this week, up 25% on 2014.