Bouazza made 101 appearances for Watford and scored 13 goals, seven of which came during last season's Barclays Premiership campaign.
The French-born Algerian international is a product of the club's academy system and manager Boothroyd warned Fulham he is not yet the finished article.
"We're disappointed to lose Hameur because I wanted to keep him in the squad for this season," Boothroyd told the club's official website.
"Sometimes though you have to weigh up the money on offer and the value a player brings to the squad who wouldn't necessarily be starting each and every week.
"He is definitely a terrific player in my eyes but has got an awful long way to go to be all he can be in his career."