Club owner Jerry Jones said Garrett had signed a four-year contract to coach the Cowboys.
"He passed the test," Jones said. "He has my respect. Jason will have the final say on any person that leaves the coaching staff or comes to the coaching staff. There won't be a player on this team that Jason does not want on the team. That's the way we're going to operate.
"I wanted to make sure our fans knew the extent of his power. Let's not be naive. You know that I'm criticized for making decisions in areas where fans and other people would like coaches to make. That's the reason that I'm being as definitive as I am about this."
Garrett took over the team after Coach Wade Phillips was fired in the middle of the season. The Cowboys responded with a 5-3 mark the rest of the way, with the three losses being by a total seven points.
Garrett, 44, was a backup quarterback with the Cowboys for seven years and has been an assistant coach since 2007.