Murray was born in Bedford, Texas to Kevin Murray and Misun Henderson.He attended Allen High School in Allen, Texas. As a senior in 2014, he was the Gatorade Football Player of the Year.His team won three straight state championships and 43 games in a row. He missed one start during this streak and finished his career with a perfect 42–0 record as a starting quarterback.

Murray was ranked by ESPN, Scout.com, and 247Sports as a five-star recruit and the best dual-threat quarterback in his class.In May 2014, he committed to Texas A&M University to play college football and college baseball.He officially signed with them on February 4, 2015.

Murray also plays baseball and was considered one of the top prospects for the 2015 Major League Baseball draft. In high school, Murray was a shortstopand a second baseman. He was the first player to ever be selected for both the Under Armour All-America Baseball Game and Under Armour All-America Football Game. Murray opted out of the MLB draft after deciding to attend Texas A&M.He was initially set to play as an infielder for the Texas A&M Aggies baseball team in the 2016 season until he announced his departure from Texas A&M on December 17, 2015.

Texas ATM

As a true freshman in 2015, Murray competed with Kyle Allen before the season for the starting quarterback position. Allen won the job, with Murray appearing in games as a backup (primarily on plays involving the wildcat formation).After the team lost two straight games in October, the competition was opened again prior to the South Carolina game, and Murray won the starting quarterback position. In his first start, Murray threw for 223 yards and rushed for 156 yards with a ing touchdown and a rushing touchdown, making him and Cam Newton the only SEC quarterbacks in the past 20 years to gain over 100 yards ing and rushing, including a ing touchdown and a rushing touchdown in their first career start. On December 24, 2015, Murray announced that he was transferring to University of Oklahoma. He sat out the 2016 season per NCAA transfer rules.

Oklahoma 2017

In the 2017 season, Murray was a backup quarterback to Baker Mayfield. He got the opportunity to play in some games in relief of Mayfield. He made his season debut in the season opener against UTEP. In the 56–7 victory, he came into the game in the second half and finished 10-of-11 for 149 yards and a touchdown.Two weeks later, against Tulane, he hit all three attempts for 103 yards and a touchdown.On November 25, against West Virginia, he started the game after Mayfield had to sit out some of the game due to disciplinary actions in the previous game against Kansas. In the game, he hit both attempts for 52 total yards and a touchdown while contributing 80 rushing yards on three carries.

Murray played for the Oklahoma Sooners baseball team in 2017 as a left fielder. He had a .122 batting average and six runs batted in (RBIs) in 27 games. In 2018, playing as a centerfielder, Murray batted .296 with 10 home runs, 47 RBIs, and 10 stolen bases.

Despite Murray's reported intention to continue his football career, the Oakland Athletics selected Murray with the ninth overall selection of the 2018 MLB draft.He signed a contract with the Athletics which includes a $4.66 million g bonus.Murray played football in his junior year, but will report to spring training in 2019 to begin his professional baseball career.

Oklahoma 2018

Murray threw for more than 4,000 yards and 40 touchdowns in the 2018 regular season. In December 2018, Murray was awarded the prestigious Heisman Trophy as the best collegiate football player in the country, giving OU back-to-back Heisman winners in Baker Mayfield in 2017 and Murray in 2018.