DeBoer, who came to Washington after two seasons at Fresno State, has known Penix since 2019, when DeBoer was the offensive coordinator and quarterbacks coach at Indiana. Current Washington tight ends coach Nick Sheridan, the Hoosiers' offensive coordinator over the past two seasons, also coached Penix.
"Michael's had a great camp," DeBoer told ESPN on Monday, prior to announcing his decision. "There's a good familiarity with the offense for Penix. It's been good. He's had a full offseason to really work out and get stronger and to make sure he can have a good, healthy season."
Penix played four seasons at Indiana before entering the transfer portal Dec. 5. He was the Hoosiers' starter for three seasons but struggled to stay on the field, suffering season-ending injuries each year, including ACL injuries in 2018 and 2020.
Penix played five games in 2021 before separating an AC joint in his throwing shoulder. He finished the season with 939 yards passing, 4 touchdowns and 7 interceptions.
Morris started last season as the Huskies went 4-8. He threw for 2,458 yards, 14 touchdowns and 12 interceptions in 11 games.
Washington opens the season against Kent State on Sept. 3.
DeBoer said his more spread-based offense has improved over the past week and a half.
"It starts up front with the offensive line," DeBoer said. "I think it's really come together and that helps our quarterback play out -- get a little more time in the pocket -- and the run game continues to improve. Getting used to more spread sets and a little more space has been something they've steadily gotten used to."
ESPN's Paolo Uggetti and Heather Dinich contributed to this report.