Both made their announcements via social media.
Darnold released an Instagram video thanking his friends and family, as well as the coaching staff at USC and San Clemente High School.
Rosen released a statement via Twitter thanking the UCLA community and ending with "P.S. Mom - I promise I will come back and finish my degree."
Darnold took over as the Trojans' starting quarterback four games into last season as a redshirt freshman. He won the Rose Bowl in his first season with a record 453-yard, five-touchdown performance against Penn State, and he led the Trojans to their first Pac-12 championship since 2008 this season.
Darnold passed for 7,229 yards with 57 touchdown passes and 22 interceptions in 27 games behind center for the Trojans.
Rosen has been the Bruins' starting quarterback for the past three seasons, playing in 30 total games after missing half of his sophomore year with injuries. He passed for 9,301 yards with 59 touchdown passes and 26 interceptions.
Despite his performance, UCLA had a disappointing season, finishing 6-7 and losing in the Cactus Bowl to Kansas State. Rosen didn't play in that game.
He was close to fired UCLA coach Jim Mora, but discussed his decision with new Bruins coach Chip Kelly.
In his statement, Rosen says that attending UCLA was "the best decision of my life."
The Associated Press contributed to this report.