Weaver, who played for the team from 2006 to 2008, had been the defensive line coach since 2016.
Weaver played for Rex Ryan with the Baltimore Ravens from 2002 to 2005 prior to playing for the Texans.
Crennel's contract expires soon and he could retire, or return as a senior assistant, similar to his role in 2017 when Mike Vrabel was defensive coordinator.
Crennel first became the Texans' defensive coordinator in 2014, when Bill O'Brien was hired as head coach. Crennel returned to that role after Vrabel left to become the Tennessee Titans head coach in 2018.
According to SportsRadio 610 insider John McClain, the decision to promote Weaver had been expected since last week's loss to Kansas City in the AFC Divisional Game.
Weaver, McClain said, is highly thought og as a defensive coordinator and possible head coach.