Amundson was born in Ventura, California, and grew up in Boulder, Colorado.
He played college basketball at UNLV from 2001 to 2002 and then from 2003 to 2006, missing the 2002–03 season as a medical redshirt due to a thumb infection.
Amundson has played in the NBA D-League and was named the NBA D-League Rookie of the Year in 2007.
On March 8, 2007, Amundson signed a 10-day contract with the Philadelphia 76ers.
On August 14, 2008, Amundson signed a two-year contract with the Phoenix Suns. On June 30, 2009, Suns exercised the team option on Amundson's contract.
On September 13, 2010, Amundson signed a two-year $4.17 million contract with the Golden State Warriors, with the second year being a player option. During 46 games, he averaged 4.3 points and 4 rebounds in 15 minutes of play. After the 2010–2011 season, he exercised his option to stay with the Warriors for one more year.
On October 16, 2010, in a game against the Trail Blazers in Portland, Amundson dislocated the middle knuckle on his right index finger and had a fracture at its base that required surgery.
On October 18, 2010, Amundson underwent successful surgery to repair this fractured right index finger. The procedure was performed by Dr. Andrew Gutow, a hand specialist from the Palo Alto Medical Foundation, at the Menlo Park Surgical Hospital.
On December 19, 2011, Amundson was traded to the Indiana Pacers for Brandon Rush.
On March 13, 2012, Amundson helped avenge his broken finger from the prior season when he was with Golden State and scored a career-high 21 points to help Indiana beat the Portland Trail Blazers 92–75.
He signed with the Minnesota Timberwolves on September 25, 2012. He was waived by the Timberwolves on February 8, 2013.
On March 2, 2013, the Chicago Bulls signed Amundson to a 10-day contract.
On March 12, 2013, Amundson signed with the New Orleans Hornets for the rest of the 2012–13 NBA season.
On September 30, 2013, Amundson signed with the Los Angeles Clippers. On October 26, 2013, he was waived by the Clippers.
On November 12, 2013, Amundson signed with the New Orleans Pelicans for the rest of the 2013–14 NBA season. On December 31, 2013, he was waived by the Pelicans.
On April 10, 2014, Amundson signed with the Chicago Bulls for the rest of the 2013–14 season. On July 15, 2014, he was waived by the Bulls.
On September 26, 2014, Amundson signed with the Cleveland Cavaliers.
On January 5, 2015, Amundson was traded to the New York Knicks in a three-team trade that also involved the Cavaliers and the Oklahoma City Thunder. The Knicks received Amundson, Alex Kirk, and a second round pick in the 2019 NBA draft, while Cleveland received Iman Shumpert and J. R. Smith from the Knicks and a first round pick in the 2015 NBA draft from the Thunder, while Cleveland sent Dion Waiters to Oklahoma City, and the Thunder send Lance Thomas to the Knicks. After being waived by the Knicks on January 7, he signed a 10-day contract with the team three days later. With his Knicks debut on January 15, he became just the twelfth player to play for at least ten NBA teams. On January 20, he signed a second 10-day contract with the Knicks. On January 30, he signed with the Knicks for the rest of the season.
On July 30, 2015, Amundson re-signed with the Knicks. He re-signed with the Knicks for a second time on September 19, 2016, but was later waived on October 21, 2016.
On March 23, 2017, Amundson signed with TNT KaTropa of the Philippine Basketball Association as an import for the 2017 PBA Commissioner's Cup. He appeared in two games for TNT KaTropa before parting with the team on March 27.
Amundson has Swedish heritage on his father's side, and also lived in Stockholm for a time. He expressed a desire to play for the Swedish national team, but that failed when the Swedish immigration ministry rejected his application for citizenship.