Born in Rocky Mountain House, Alberta, Brad Stuart excelled in the WHL with the Regina Pats and Calgary Hitmen. In 1999 he was named to the CHL First All-Star team and named the country's top junior defenceman. Stuart was chosen third overall by the San Jose Sharks in 1998 and scored ten goals as an NHL rookie.
A member of Canada's 1999 silver medal World Junior Team, Stuart saw his offensive numbers drop in 2000-01, however his defensive game improved. Even with his point totals dipping, Stuart's strong play defensively earned him an invite to play for Team Canada at the 2001 World Championships.
Having only missed a total of five games in his first three seasons, Stuart's 2002-03 season would be plagued by injuries, limiting him to a mere 36 games. In 2003-04, Stuart established a career high in points with 39 (9-30-39), while helping the Sharks reach the Western Conference Final, only to come up short against a determined Calgary Flames squad.
Following a lockout year in 2004-05, Stuart returned to San Jose in the fall of 2005, yet was shipped to the Boston Bruins in the early stages of the season along with Wayne Primeau and Marco Sturm for Joe Thornton.
In his first half-season as a member of the Boston Bruins, Stuart would set a career high in points with 43 (12-31-43). Despite his offensive production with the B's, Stuart was traded with Wayne Primeau to the Calgary Flames in exchange for Andrew Ference and Chuck Kobasew.
Stuart's stint in Calgary lasted only 27 games as the free agent defenseman signed a one-year contract with the Los Angeles Kings in the summer of 2007. He went on to compete in 63 games with the Kings, but struggled to produce offensively. At the NHL trading deadline, the Detroit Red Wings were looking to bolster their depleted blueline and add a key player to their power-play and penalty-killing units. As a result Stuart was dealt from the Kings to the Red Wings for a pair of draft picks. After completing the regular season with his new club, he suited up for 21 games of the Detroit's drive to the Stanley Cup in 2008.
On June 10, 2012, Stuart's rights was traded to the San Jose Sharks for Andrew Murray and a seventh round draft pick. He was then signed to a three year contract eight days later.
During the offseason of 2014, the Sharks traded Stuart to the Colorado Avalanche for a second and sixth round draft pick.