Garrett spent the previous two seasons as the quarterbacks coach of the Miami Dolphins. He joined the Cowboys staff on Jan. 25, but at that point the team didn't have a head coach.
The Cowboys gave Wade Phillips the job as head coach on Feb. 8.
"We believe that Jason is one of the bright young offensive minds in the NFL," Phillips said. "He has extensive experience in working with some outstanding offensive coaches through 16 years of professional football, and he is well prepared for this position."
The Cowboys also named Tony Sparano assistant head coach on Tuesday. He will continue to handle the responsibilities of coaching the Cowboys offensive line. Sparano agreed to a contract extension that will keep him with the organization through at least the 2009 season.