Smith said Koetter will bring "a fresh set of ideas to our offense."
"He is bright, he understands the intricacies of the vertical passing game, but he also wants to be able to run the football which is very important in the NFL," Smith said. "I look forward to working with Dirk and have tremendous confidence that he will be a great addition to our team and our coaching staff."
Smith has emphasized a run-first philosophy with Atlanta.
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.
Koetter, 52, was a combined 66-44 as the head coach at Boise State (1998 to 2000) and Arizona State (2001-06).
With Atlanta, Koetter inherits an offense blessed with established starters such as quarterback Matt Ryan, running back Michael Turner, tight end Tony Gonzalez and receivers Roddy White and Julio Jones. With the exception of Jones, who was a breakout rookie in 2011, all those playmakers, plus fullback Ovie Mughelli, have been Pro Bowl selections.
Despite the wealth of talent, the offense was a disappointment as the team suffered its third straight playoff loss in its four years with Smith.
That trade leaves the Falcons fewer draft picks this year to address problem areas on the offense, including on the offensive line.
A phone message was left seeking comment from Koetter.