Rosen was selected 10th overall in the 2018 NFL draft by the Arizona Cardinals, and served as the team's starter during the majority of his rookie season.

[2] Rosen's father is Jewish and was a nationally ranked ice skater who almost qualified for the Winter Olympics in the 1970s, and his mother is a Quaker, who was the captain of the Princeton lacrosse team.

[15] He was also named the Southern California Jewish Sports Hall of Fame's Male High School Athlete of the Year.

[19] He verbally committed to the University of California, Los Angeles (UCLA) in March 2014 before officially signing in September.

[3][11] With three-year starting quarterback Brett Hundley leaving UCLA early for the NFL, a large hole was created on the team.

[11][24][25][26] On August 26, a week after being publicly criticized by head coach Jim Mora, Rosen was named the Bruins' starting quarterback.

The victory kept UCLA in contention for the Pac-12 championship entering their regular-season finale against their crosstown rivals, the USC Trojans.

[15] In 2016, Rosen was injured in an October 8 loss to Arizona State Sun Devils, when he threw for a then-career high 400 yards.

[40] In the 2017 season opener at the Rose Bowl in Pasadena, California, Rosen completed 35-of-59 passes for 491 yards and four touchdowns to rally UCLA to a 45–44 win over Texas A&M, capped off by a touchdown pass to Jordan Lasley on a fake spike play with 48 seconds to go in the game.

[41] The Bruins overcame a 34-point deficit, the largest comeback in school history and the second-most ever in the Football Bowl Subdivision (FBS).

[40] After missing one game, Rosen returned to the lineup and threw for 381 yards with one touchdown and also scored on a one-yard run in a 44–37 win over the Arizona State Sun Devils.

[49] In his first matchup against USC quarterback Sam Darnold, Rosen was 32 of 52 passing for 421 yards along with three touchdowns and an interception in a 28–23 loss to the Trojans.

[50][51] In the regular season finale against California, Rosen led the Bruins to a 17–9 lead at the half, but was held out the rest of the game after suffering his second concussion.

He made his first regular season appearance in Week 3 of 2018, replacing starter Sam Bradford with 4:31 remaining against the Chicago Bears and the Cardinals trailing 16–14.

[68] Entering the game, the Cardinals had scored just six points and ranked last in a number of offensive categories,[67] but jumped out to a 14–0 first quarter lead before six scoreless possessions prompted Arizona coach Steve Wilks to switch to Rosen.

[72] In Week 7, Rosen had two of his three interceptions returned for touchdowns, lost two fumbles, and was sacked six times in a 45–10 loss to the Denver Broncos on Thursday Night Football.

He threw a career-high 252 passing yards and two touchdowns, including the game-winning score to Kirk with 34 seconds remaining to rally the team from a 15–3 fourth-quarter deficit.

[78] He praised his teammates during the season, and resisted criticizing the team's unimaginative playcalling or weak offensive line and receiving corps.

[82][83] Arizona general manager Steve Keim attributed the trade to the value they received and said that "all of us are big fans of Josh Rosen".

[87] After relieving Fitzpatrick in both contests,[88][89] Rosen was named the starter for Week 3,[87] and threw for 200 yards as the Dolphins lost 31–6 to the Dallas Cowboys.

Rosen was unable to surpass either Tagovailoa or Fitzpatrick on the depth chart, and Miami waived him on September 5 after failing to find a trade partner.

[99] On August 17, 2021, after struggling to compete for the third quarterback spot behind Garoppolo and 2021 first round draft pick Trey Lance, Rosen was waived by the 49ers.

[101][102] He was named the second-string option for the season opener behind incumbent starter Matt Ryan and ahead of undrafted rookie Feleipe Franks.

[103] Rosen made his season debut during Week 2 against the Tampa Bay Buccaneers when he replaced Ryan for the Falcons' final drive.

[105] The following week against the New England Patriots, Rosen made a third relief appearance in the fourth quarter after Ryan threw two interceptions on consecutive drives.

Rosen completed one of two pass attempts before throwing an interception to linebacker Kyle Van Noy that was returned for a touchdown.

The Cardinals, Dolphins, and 49ers each spent a first-round draft pick on a quarterback the year after playing Rosen before cutting or trading him.