Richardson grew up in Belleville, Ontario playing minor ice hockey for the AA Belleville Bobcats and eventually for the AAA Quinte Red Devils of the OMHA. He played in the 1998 Quebec International Pee-Wee Hockey Tournament with the Quinte team. After a strong season in Bantam, Richardson was the 1st round choice in the 2001 OHL Priority Selection by the Owen Sound Attack. Richardson was drafted by the Colorado Avalanche in the 2003 NHL Entry Draft. He was the chosen 163rd overall in the 5th round from the Owen Sound Attack of the Ontario Hockey League. Brad played his first professional season in the 2005–06 season, splitting the year between the Lowell Lock Monsters of the AHL and making his debut in the NHL with the Avalanche. Richardson's best year with the Avalanche came in the 2006–07 season, playing in a career high 73 games, recording 14 goals and 22 points. On June 21, 2008, Richardson was traded from the Avalanche to the Los Angeles Kings for a second round pick. On September 15, 2008, Richardson signed with the Kings for two years and $1.175 million. Richardson achieved his first career hat trick on October 23, 2010, against his old team, the Colorado Avalanche, in a 6-4 Kings victory. On July 12, 2011, Richardson re-signed on a two-year contract extension worth $2.35 million with the Kings. In the 2011–12 season, in a utility role he played in 59 regular season games for 9 points before capturing the Stanley Cup with the Kings whilst featuring in 13 post-season games. Richardson missed the first two post-season games that year after undergoing an emergency appendectomy. On July 5, 2013, Richardson signed as a free agent to a two-year contract worth $1.15 million per year by the Vancouver Canucks. Richardson as a free agent for the second time in his career, signed a three-year contract with the Arizona Coyotes on July 1, 2015. During his second season with the Coyotes in 2016–17 in the midst of a productive start to the campaign with 9 points in 16 appearances, he was hit by defenceman Nikita Tryamkin in a game against his former club, the Vancouver Canucks on November 17, 2016. He suffered a fractured tibia and fibula bones in his right leg, requiring season ending surgery. On July 3, 2018, Richardson re-signed with the Coyotes on a two-year deal worth $2.5 million.
