Born in Los Angeles, Johnson grew up mainly in South Central Los Angeles, but also spent time as a child in Harbor City and Watts. Despite being tall and athletic, Johnson struggled to find a place on a high school basketball team. His freshman year was split at two schools (Pacific Hills, Narbonne), neither of which featured him on the court. From there, he enrolled at Verbum Dei High School, where he enjoyed a solid inaugural season of high school basketball as a sophomore in 2002–03. He then transferred to Westchester High School but was forced to sit out his junior year of 2003–04. He made up for lost time as a senior in 2004–05 as he was named the 2005 California Mr. Basketball after leading Westchester to a state title. He was subsequently named a McDonald's All-American and appeared in the 2005 Boys Game.
Considered a four-star recruit by Rivals.com, Johnson was listed as the No. 7 power forward and the No. 29 player in the nation in 2005.
Despite committing to play for the University of Louisville, Johnson decided to skip college and declared for NBA draft.
Johnson was selected by the Detroit Pistons with the 56th overall pick in the 2005 NBA draft. He is the last direct from high school player to be selected in the NBA draft (until 2015 with Satnam Singh Bhamara), as the NBA instituted a rule prior to the 2006 draft that requires American players to be at least one year removed from the graduation of their high school class to be eligible.
As a rookie for the Pistons, Johnson appeared in just three games during the 2005–06 season. He scored his first NBA basket on a windmill dunk against the Minnesota Timberwolves on January 24, 2006. On February 27, 2006, he was assigned to the Fayetteville Patriots of the NBA Development League. After appearing in 18 games for the Patriots, he was recalled by the Pistons on April 17, 2006. That same day, he scored 18 points for the Pistons in their 20-point loss to the Milwaukee Bucks, making all six of his field goal attempts, both three-point attempts, and all four of his free throw attempts.
Johnson spent most of the 2006–07 season playing for the Sioux Falls Skyforce of the NBA Development League, where he earned Player of the Week honors for his play. In 22 games for the Skyforce, Johnson averaged 18.9 points, 9.7 rebounds, 2.1 assists, 1.2 steals and 3.1 blocks per game, while shooting 62.3% from the field. Despite his strong D-League play, Johnson managed just eight games for the Pistons in 2006–07, averaging 5.9 points, 4.6 rebounds and 1.6 blocks per game.
On July 12, 2007, Johnson re-signed with the Pistons to a three-year, $12 million contract. Over the next two seasons, Johnson played a total of 124 games for the Pistons as he became a valuable asset off the bench. He averaged 3.6 points and 3.8 rebounds in 2007–08, and 3.5 points and 3.7 rebounds in 2008–09. He also averaged 1.1 blocks per game over the two seasons.
On June 23, 2009, Johnson was traded to the Milwaukee Bucks in a three three-team trade that also involved the San Antonio Spurs and Richard Jefferson. He was later traded to the Toronto Raptors on August 18, 2009, along with Sonny Weems, in exchange for Carlos Delfino and Roko Ukić.
On July 8, 2010, Johnson re-signed with the Raptors to a five-year, $34 million contract.
Johnson had a career-best season in 2012–13 as he averaged career-highs in minutes played (28.7 mpg), points (10.0 ppg), rebounds (7.5 rpg), assists (1.5 apg) and steals (1.0 spg). With his continued rise in dominance and overall production, Johnson began to embrace the city of Toronto, quoting that “Toronto is part of me. I've been around, the people are very kind, I love it here.”
On December 8, 2013, Johnson scored a career-high 32 points in a 106–94 win over the Los Angeles Lakers.
On July 9, 2015, Johnson signed a two-year, $24 million contract with the Boston Celtics. He made his debut for the Celtics in the team's season opener against the Philadelphia 76ers on October 28, recording 15 points and 7 rebounds off the bench in a 112–95 win. On January 13, 2016, he recorded 14 points and a season-high 18 rebounds in a 103–94 win over the Indiana Pacers. On March 20, he scored a season-high 18 points in a 120–105 win over the Philadelphia 76ers. He finished the 2015–16 season with averages of 7.3 points and 6.4 rebounds per game.
On November 2, 2016, Johnson scored 23 points and hit a career-high four three-pointers in a 107–100 win over the Chicago Bulls.
On July 8, 2017, Johnson signed a one-year deal with the Philadelphia 76ers.
Johnson grew up in an athletic family. His sister, Indi, played forward for Southern University's women's basketball team, while his cousins, Kevin and Kaelin Burnett, both play linebacker in the NFL.
Johnson is highly involved in community work, and regularly hosts back to school programs, visits local hospitals and pays for low income youth to attend games. He is also known for his random acts of kindness. Shortly after the release of Drake’s Nothing Was the Same album, Johnson bought all the copies from two local stores and handed them out to random pedestrians in Toronto.