Harrell, a 6'8" power forward from Tarboro, North Carolina, starred at North Edgecombe High School before prepping for a year at Hargrave Military Academy in Chatham, Virginia. There he led the team to a 38–1 record while averaging 25.2 points and 13.6 rebounds per game. Originally Harrell committed to play college basketball for coach Seth Greenberg at Virginia Tech, but after Greenberg was fired, Harrell was released from his commitment and chose Louisville.
As a freshman, Harrell backed up power forward Chane Behanan, averaging 5.7 points and 3.6 rebounds in 16.2 minutes per game. He played his best at the end of the season, scoring 20 points in the Cardinals' Big East Conference championship victory over Syracuse. In his reserve role, Harrell helped the Cardinals win the 2013 NCAA championship to cap his freshman season.
With Gorgui Dieng's departure for the 2013 NBA draft, Harrell received recognition in the offseason leading to his sophomore year as one of the top returning players in the country. The Sporting News selected Harrell to the preseason All-America third team in its 2013–14 college basketball preview magazine. Harrell decided to stay for his junior season instead of opting for the NBA.
In the 2014–15 season, Harrell averaged 15.7 points and 9.2 rebounds per game and received the Karl Malone Award for the nation's top power forward.
On June 25, 2015, Harrell was selected by the Houston Rockets with the 32nd overall pick in the 2015 NBA draft. On September 19, 2015, he signed a three-year deal with the Rockets. He made his debut for the Rockets in the team's season opener against the Denver Nuggets on October 28, recording eight points and three rebounds in a 105–85 loss. Two days later, he scored 17 points in a loss to the Golden State Warriors. On November 13, he made his first career start, scoring five points in just under 13 minutes of action, as the Rockets were defeated by the Denver Nuggets 107–98. On March 28, 2016, Harrell received a five-game suspension without pay for pushing a game official. During his rookie season, he received multiple assignments to the Rio Grande Valley Vipers, the Rockets' D-League affiliate.
On November 2, 2016, Harrell had a 17-point, 10-rebound effort off the bench in a 118–99 win over the New York Knicks. On December 21, 2016 against the Phoenix Suns, Harrell made his first start of the season and second of his career. He scored 17 points as a result, tying a career high. On December 30, he set a new career high with 29 points in a 140–116 win over the Los Angeles Clippers. On January 8, 2017, he had 28 points in 26 minutes off the bench on 12-of-13 shooting in a 129–122 win over the Toronto Raptors.
On June 28, 2017, the Los Angeles Clippers acquired Harrell, Patrick Beverley, Sam Dekker, Darrun Hilliard, DeAndre Liggins, Lou Williams, Kyle Wiltjer and a 2018 first-round pick from the Houston Rockets in exchange for Chris Paul.
In 2012, Harrell was a member of the United States team at the FIBA Americas Under-18 Championship that won Gold in São Sebastião do Paraíso, Brazil.
He is the son of Samuel and Selena Harrell and has two younger brothers, Cadarius and Quatauis. He majored in sports medicine.