Andersen is the second of the three children of corrections officer and Danish immigrant Claus Andersen and Linda Holubec, a Tennessee native who worked as a waitress at the Port Hueneme base, and played basketball in high school. In 1982, when Andersen was four, his family moved to Texas, using a loan from the Texas Veterans Land Board to purchase a 10-acre plot in unincorporated Iola, about 100 miles north of Houston. Shortly later, Claus left the family without finishing the house they were building. The Andersens then lived off the land, with Linda working on low-end jobs and relying on the help of neighbors and Linda's brother, who was a Navy supply boat captain. During Andersen's middle school years, he and his siblings were sent to a group home in Dallas for three years.
During high school, Andersen was convinced to take up basketball by the varsity basketball coach, who said the sport could give him a chance at a college scholarship. Andersen could not get the grades to attend the University of Houston, but went to Blinn College in Brenham, where the coach was the father of Andersen's high school coach. He played one season with the Blinn Buccaneers, leading the National Junior College Athletic Association players in Blocks.
Convinced that he could play professionally, Andersen dropped out of Blinn in 1999, not knowing he had to officially apply for the NBA draft to get picked up. Andersen's high school coach arranged for him to play a series of exhibition games with the semi-professional Texas Ambassadors, and a game in China led Andersen to get an offer to join the Jiangsu Nangang Dragons of the Chinese Basketball Association. In March 2000, he joined the New Mexico Slam of the International Basketball League where he averaged just 1.1 points and 1.6 Rebounds in six regular season games and four playoff games. Later that year, he joined the Dakota Wizards of the IBA but left before the season started. He then joined the Fargo-Moorhead Beez also of the IBA where he played seven games before being released in January 2001. Later that year, he joined the Sugarland Sharks of the Southwest Basketball League.
In July 2001, Andersen joined the Cleveland Cavaliers for the 2001 NBA Summer League. On September 28, 2001, he signed with the Phoenix Suns. However, he was later waived by the Suns on October 7, 2001. On October 31, 2001, he was selected with the first overall pick by the Fayetteville Patriots in the NBA Development League's inaugural draft.
Andersen became the first D-League player called up by an NBA team, signing with the Denver Nuggets on November 21, 2001 after just two games for Fayetteville. He quickly became one of the top per-minute rebounders and shot-blockers in the league. During the 2002 Rocky Mountain Revue, teammates Junior Harrington and Kenny Satterfield nicknamed Andersen "Birdman" for his arm span and penchant for aerial acrobatics.
On September 29, 2003, he re-signed with the Nuggets.
On July 19, 2004, Andersen signed a multi-year deal with the New Orleans Hornets. He appeared in the NBA Slam Dunk Contest during the 2005 All-Star Weekend for the second year in a row, where he unsuccessfully tried the same dunk eight times at the Pepsi Center.
Following the effects of Hurricane Katrina in August 2005, the Hornets moved to Oklahoma City for the 2005–06 season and temporarily became the New Orleans/Oklahoma City Hornets. In 2005–06, Andersen managed just 32 games (two starts), averaging 5.0 points and 4.8 rebounds per game.
On January 25, 2006, Andersen was disqualified from the NBA for violating the league's anti-drug policy by testing positive for a banned substance. Andersen's suspension fell under the league's category of "drugs of abuse", violation of which is possible grounds for expulsion from the NBA under the league's collective bargaining agreement. Andersen attempted to appeal the ruling through arbitration, but the arbitrator ruled to uphold his dismissal in March 2006. As Andersen waited for his reinstatement effective which could be given in January 2008, he was helped by a lawyer friend in Denver, Mark Bryant, who became his adviser. Andersen spent a month in a rehab clinic in Malibu, and worked out and coached a boys' basketball team in Denver.
On March 4, 2008, the NBA Players Association granted Andersen's request to be reinstated as an NBA player. The reinstatement was effective immediately, and the rights to his services belonged to his former team, the New Orleans Hornets, who re-signed him on March 5, 2008 for the rest of the 2007–08 season.
On July 24, 2008, Andersen signed a one-year deal with the Denver Nuggets. Andersen finished the 2008–09 season second in the league in blocks per game with 2.5 despite playing only 20.6 minutes per game.
On July 8, 2009, Andersen re-signed with the Nuggets on a five-year deal.
On July 17, 2012, the Nuggets waived Andersen via the amnesty clause. Nuggets General Manager Masai Ujiri, a friend of Andersen, reluctantly made the transaction in order to remove $9 million from the team's payroll cap to avoid the luxury tax.
Before he was waived by the Nuggets, Miami Heat head coach Erik Spoelstra had repeatedly lobbied Pat Riley to acquire Andersen.
On January 20, 2013, Andersen signed a 10-day contract with the Miami Heat. He was signed to a second 10-day contract on January 30, and signed for the remainder of the season on February 8, 2013.
Andersen played in only 42 games during the 2012–13 season but still contributed to the Heat's success by putting up 4.9 points per game on 57.7 FG% and 4.1 rebounds in 14.9 minutes of play. After he joined the Heat, his team went on a 27-game winning streak, overall going 37-3 in regular-season games in which Andersen played. Andersen also gained legions of fans inspired by his head-to-toe tattoos, Mohawk haircut, and trademark hustle.
Andersen shot 15-15 in Games 1-5 against the Indiana Pacers in the Eastern Conference Finals, including a 7-for-7 performance in Game 1 that set a franchise playoff record, besting the 6-for-6 mark by Alonzo Mourning in 2007. Andersen was suspended for Game 6 of the 2013 Eastern Conference Finals without pay for committing a flagrant foul on Tyler Hansbrough in Game 5.
At age 34, he reached the NBA Finals for the first time in his career. Against the San Antonio Spurs in the deciding Game 7 of the 2013 NBA Finals, Andersen recorded three points, four rebounds, and a block en route to his first NBA championship. With a Field goal percentage of 80.7%, Andersen finished the 2013 NBA Playoffs with an NBA Playoffs record for highest field goal percentage.
On July 10, 2013, Andersen re-signed with the Miami Heat. He played 72 games during the 2013–14 regular season, averaging 6.6 points, 5.3 rebounds and 1.3 blocks per game. On May 26, 2014, before Game 4 of the Eastern Conference Finals, it was announced that Andersen would miss Game 4 and subsequently Game 5 due to an array of nagging aches and pains which he had been suffering for some time. Andersen returned for Game 6, recording 9 points and 10 rebounds as the Heat went on to advance to their fourth straight NBA Finals and Andersen's second. The Heat again faced the Spurs in the 2014 NBA Finals, but were defeated in five games.
On July 19, 2014, Andersen again re-signed with the Heat. Over the course of the 2014–15 regular season, Andersen started 20 games, the most in a single season of his career.
On February 16, 2016, the Heat traded Andersen and two second-round picks to the Memphis Grizzlies in a three-team trade also involving the Charlotte Hornets. Three days later, he made his debut for the Grizzlies in a 109–104 win over the Minnesota Timberwolves, recording four points, three rebounds and one block in 11 minutes.
On July 22, 2016, Andersen signed with the Cleveland Cavaliers. On December 16, 2016, he was ruled out for the rest of the season after suffering an ACL tear that required season-ending surgery.
On February 13, 2017, the Cavaliers traded Andersen and cash considerations to the Charlotte Hornets in exchange for a 2017 protected second-round pick. He was immediately waived by the Hornets upon being acquired.
Andersen is known for brightly colored tattoos on his arms, chest, neck, back, hands and legs. His first tattoo was given as an eighteenth birthday gift by his mother, who has some body art of her own from her tenure in the Bandidos Motorcycle Club. Andersen's regular tattoo artist, Denver-based John Slaughter, estimates he has inked 65 percent of his body. He showed off those tattoos in PETA's "Ink Not Mink" ad campaign to protest the fur industry.
On May 10, 2012, Denver NBC affiliate 9News reported that Andersen's home was the target of an investigation of a suspected Internet criminal case by the Douglas County Sheriff's Office Internet Crimes Against Children Unit. Andersen was not charged with any crimes. In September 2013, it was revealed that Andersen was the victim of an elaborate hoax, orchestrated by a Canadian woman in Easterville, Manitoba.