He played college football for the UCLA Bruins and Oregon State Beavers before signing with the Dallas Cowboys as an undrafted free agent in 2007.

[1] As a junior, Moore lettered in football while playing as a safety, earning All-CIF acclaim with 80 tackles and 10 interceptions on the season.

Moore led his team to a 13–0 record, culminating in a 42–13 win over Valencia in the CIF-Southern Section Division III title game.

The Bruins defeated Stanford in Moore's debut, making him the first true-freshman QB in his first game to lead UCLA to victory.

He moved back in front of Olson on the depth chart for the Oct 26 game at the Rose Bowl against Arizona State, passing for 190 yards and a touchdown in UCLA's 20–13 win.

Making yet another record-breaking debut, he threw for 367 yards in the season opener against Portland State, the most ever by a Beaver quarterback in his first start.

[13][14][15] He hit Mike Hass on a 63-yard touchdown strike against Washington State that gave OSU the lead 37–33 after the team trailed 30–13 late in the second quarter.

[19] He set an Oregon State record for the most consecutive pass attempts without an interception with 183 before having that streak end in the Sun Bowl.

Moore's first NFL completion was a 43-yard pass to Keary Colbert; his playing time was brief as Carr returned to the field for the game's second half.

[30] As a result of Delhomme's season-ending surgery and Carr's back injury, the Panthers signed veteran quarterback Vinny Testaverde to their roster.

[33] After six brief appearances during the season, Moore started his first NFL game on December 16, 2007, against the Seattle Seahawks; Testaverde was ruled unable to play, because of "general soreness.

[34] The following week, the Panthers suffered a loss against the Cowboys, while Moore had 15 completions on 28 pass attempts for 182 yards, a touchdown, and an interception.

[36] The Panthers ended the season with a road win against the Tampa Bay Buccaneers, in which Moore completed 15 of 24 pass attempts for 174 yards, two touchdowns, and an interception.

[26] Moore saw his first action of the 2009 season when backup quarterback Josh McCown was injured during the Panthers' week 1 loss to the Philadelphia Eagles.

[46] He drew praise from head coach John Fox and top receiver Steve Smith, who caught nine passes from Moore for 157 yards and a score.

[47] On December 27 Moore completed 15 passes on 20 attempts for 171 yards, and for the second week in a row, three touchdowns and no interceptions, as Carolina beat the New York Giants 41–9.

[56] Though Moore had clearly established himself as the Panthers' number one quarterback, he faced pressure for the starting job from Clausen, possibly resulting in his poor play throughout the rest of the season.

Moore suffered a concussion during the season opener at the New York Giants, and he was benched the following week in a loss against the Buccaneers following poor play.

[57] On September 20, 2010, Moore was removed as the Panthers' starting quarterback in favor of rookie Jimmy Clausen, after throwing four interceptions in the first two games.

[58] After sitting out for three straight games, Moore was again declared the Panthers' starting quarterback on October 18, 2010, following poor play by Clausen.

[63] On November 6 he became the first Miami quarterback since Chad Pennington in 2008 to throw three touchdown passes in a game, in their 31–3 win over the Kansas City Chiefs.

In the 44–26 victory over the Houston Texans, he completed one pass for 14 yards and ran out the clock at the end of the game in relief of Tannehill.

[74] On March 15, 2016, Moore re-signed with the Dolphins, agreeing on a two-year deal worth $3.5 million to remain a backup for Tannehill.

[80] Moore was announced the starting quarterback for the Dolphins against the Pittsburgh Steelers in the Wild Card Round of the 2017 National Football League playoffs as Tannehill did not appear to be fully recovered.

[82] Due to Cutler's injury, Moore started the week 8 game against the Baltimore Ravens, throwing for 176 yards and 2 interceptions as the Dolphins lost by a score of 40–0.

[83] During the week 11 game against the Buccaneers, Cutler took a hit to the head on the final play of the first half and was relieved by Moore, who threw for 282 yards and 1 touchdown as the Dolphins lost by a score of 30–20.

[84] Due to Cutler being in the concussion protocol, Moore started the team's next game and finished with 215 passing yards, one touchdown, and two interceptions in the 35–17 loss.

He had started working as an assistant coach for a high school football team when he signed with the Chiefs on August 26, 2019, following an injury to backup quarterback Chad Henne.

[87][88] Moore took over as the Chiefs' quarterback after Patrick Mahomes injured his knee on October 17, 2019, in a week 7 game on Thursday Night Football against the Denver Broncos.

[89] The following week, Moore started in place of the injured Mahomes against the Green Bay Packers and had 267 passing yards and two touchdowns in the 31–24 loss.