He played college football for the Tennessee Volunteers, and was selected by the Pittsburgh Steelers in the fourth round of the 2017 NFL draft.

Dobbs has been a member of eight NFL teams during his career, including as the starter for the Tennessee Titans, Arizona Cardinals, and Minnesota Vikings.

[2] Dobbs has alopecia areata, an autoimmune disease causing hair loss, which began when he was transitioning from elementary to junior high school.

[7] Sources: As a true freshman at the University of Tennessee in 2013, Dobbs played in five games with four starts after starter Justin Worley suffered an injury in a loss against the #1 Alabama Crimson Tide at Bryant–Denny Stadium.

Dobbs performed well in the 34–20 defeat by recording 192 passing yards and two rushing touchdowns against the Crimson Tide.

Dobbs received two Offensive Player of the Week honors from the Southeastern Conference (SEC), both of which came from his combined passing and rushing performances for over 400 yards in each game.

[39] In the 20–13 overtime win, Dobbs had 192 yards passing but fumbled on the goal line; the ball was recovered by teammate and running back Jalen Hurd to give Tennessee the go-ahead score.

[42] Dobbs's last touchdown was a Hail Mary throw to wide receiver Jauan Jennings as time expired.

[47] In the final game of his Tennessee career, Dobbs led the Volunteers past the #24 Nebraska Cornhuskers by a score of 38–28 in the 2016 Music City Bowl at Nissan Stadium in Nashville.

[3] The university presented him with the 2017 Torchbearer Award, the highest honor for an undergraduate student, which recognizes accomplishments in the community and academics.

Dobbs was heralded as possessing a perfect 4.0 grade point average and being named to the SEC Academic Honor Roll.

He held workouts for six teams: the Kansas City Chiefs, Tennessee Titans, Carolina Panthers, San Diego Chargers, Pittsburgh Steelers, and New Orleans Saints.

[64] He was the seventh quarterback selected, and the Steelers also drafted his former Tennessee and Senior Bowl teammate, cornerback Cameron Sutton.

[68] After two starts and four appearances during the pre-season, Dobbs spent his entire rookie season behind incumbent starter Ben Roethlisberger and long-term backup Landry Jones.

[69][70][71] Dobbs made his NFL regular season debut on October 7, 2018, in a 41–17 Steelers win against the Atlanta Falcons, as on the final play of the game, he kneeled down.

[72] On November 4, 2018, in a 23–16 Steelers Week 9 victory against the Baltimore Ravens, Dobbs completed a 22-yard pass to JuJu Smith-Schuster, after stepping in for Ben Roethlisberger, who got injured on the previous play.

[77] Dobbs was traded after Mason Rudolph won the backup job for the Steelers, and Jaguars' quarterback Nick Foles sustained a broken clavicle during the season opener and was placed on injured reserve.

[86] On December 29, with Ryan Tannehill out for the season with an injury and rookie Malik Willis underperforming, Dobbs was named the starter for the Titans Week 17 matchup against the Dallas Cowboys.

[91] On January 2, head coach Mike Vrabel announced that Dobbs would start the Week 18 matchup against the Jaguars.

Dobbs had not taken a single practice repetition for the Vikings, and had to rehearse his cadence with the team's offensive linemen during the game.

[104] He became the first quarterback in NFL history to record three touchdowns in consecutive games while playing for different teams and was named as the NFC player of the week for his performance.

[105] Dobbs during this time received increased media attention for his journeyman career and sudden unexpected success.

His nickname "The Passtronaut," referring to Dobbs' background in aerospace engineering, first appeared in October 2023 and gained prominence during this period.

[106][107] After losses to the Denver Broncos and the Chicago Bears, Dobbs was benched in the second half of the Vikings' Week 14 game against the Las Vegas Raiders after completing 10-of-23 passes for 63 yards and scoring no points for Minnesota through three quarters.

[108] He was later demoted to the third-string quarterback after head coach Kevin O'Connell announced that Jaren Hall would backup Mullens.

[111] He saw his first snaps of the season in Week 17 against the Detroit Lions after Purdy departed late in the fourth quarter with an injury.