This marks a reunion for Gaine, who worked in Buffalo during the 2017 season as the team's vice president of player personnel under current general manager Brandon Beane.
Gaine's dismissal from the Texans after just 18 months on the job, which included an AFC South division title, came as a surprise. He will continue to be based in Houston.
He adds another layer of experience to the well-regarded front office built by Beane and coach Sean McDermott, which includes another former general manager in Dennis Hickey, who serves as a senior national scout for the team.
The Texans have opted not to hire a general manager for the 2019 NFL season.