Johnson is a native of Orangeburg, South Carolina and attended Edisto High School, where his father was the varsity basketball coach. Johnson's mother, Renee Johnson, died from colon cancer when he was a teenager.
College recruitment
College career
As a sophomore, Johnson averaged 10.3 points and 6.1 rebounds per game. As a junior, Johnson was named third-team All-ACC after averaging 12.6 points and 7.8 rebounds per game. Johnson's senior season proved to be his most impressive and he collected many accolades. As a senior co-captain, Johnson led the Tar Heels to the outright ACC regular season title, as well as the ACC tournament championship. On January 4, 2016, Johnson scored 39 points and collected 23 rebounds in leading the Tar Heels in a victory over Florida State 106-90. He became the second North Carolina player in its history to score at least 39 points and grab 23 rebounds in a single game, after Billy Cunningham achieved the feat twice in 1964. He was named to the 35-man midseason watchlist for the Naismith Trophy on February 11. On March 27, 2016, Johnson set a new North Carolina school record for most double-doubles in a season. He also tied the North Carolina school record for most rebounds in a season with 399, matching Tyler Hansbrough's 2008 season. On March 29, 2016, Johnson was unanimously selected to the Associated Press' 2015-16 All-America team. Johnson finished the 2015-2016 college basketball season with 416 rebounds, setting a new UNC record for most rebounds in a season, passing Tyler Hansbrough. Brice Johnson playing some of his best basketball in college led the Tar Heels with Marcus Paige to the NCAA men's basketballchampionship game where they fell short to Villanova 77-74 where he put up 14 points and had 8 rebounds.
Professional career
Los Angeles Clippers (2016–2018)
On June 23, 2016, Johnson was selected by the Los Angeles Clippers with the 25th overall pick in the 2016 NBA draft. On July 12, 2016, he signed his rookie scale contract with the Clippers. On October 8, 2016, he was ruled out indefinitely due to a herniated disk in his lower back. On February 23, 2017, he made his professional debut in a 123–113 loss to the Golden State Warriors, recording two rebounds in two minutes off the bench. During his rookie season, Johnson had multiple assignments to the Salt Lake City Stars of the NBA Development League, pursuant to the flexible assignment rule. On April 10, 2017, he recorded his first 2 points in a 125-96 win over the Houston Rockets.
On January 29, 2018, Johnson, along with Willie Reed and Blake Griffin, was traded to the Detroit Pistons in exchange for Avery Bradley, Tobias Harris, Boban Marjanović, a future protected first-round draft pick and a future second-round draft pick. On February 8, the Pistons traded Johnson, along with a 2022 second-round draft pick, to the Memphis Grizzlies in exchange for James Ennis. On March 27, 2018, Johnson was waived by the Grizzlies.