Gattis had previously been linked to Maryland in the same capacity, but he'll join Jim Harbaugh's staff instead.
Mike Locksley, who ran the Crimson Tide's offense along with Gattis in 2018, was hired as the Terrapins' head coach in December.
Gattis is the first offensive coordinator Harbaugh has hired since taking over as Michigan's head coach in 2015. He organized the offense previously along with multiple assistants, including passing game coordinator Pep Hamilton and wide receivers coach Jim McElwain.
Alabama fielded an offensive juggernaut in 2018, ranking third in the NCAA in scoring. Michigan, meanwhile fielded the nation's 21st-ranked scoring offense.