The Falcons announced the hire today. ESPN first reported the move.
The Falcons lost both coordinators after the season. The team is still looking to replace defensive coordinator Brian VanGorder, who moved back to the college ranks to head Auburn's defense.
Mularkey, whose Falcons offense was shut out in a 24-2 playoff loss to the New York Giants, was introduced as Jacksonville's coach on Wednesday. He hired former Falcons quarterbacks coach Bob Bratkowski to be his offensive coordinator.
Koetter was a combined 66-44 as the head coach at Boise State (1998 to 2000) and Arizona State (2001-06).