Anderson attended Carlsbad High School in Carlsbad, California, where he was a star baseball player and won team MVP several times. After graduation, he studied economics at the University of California, Irvine. He played outfield and first base for the college team and left college after his junior season when he was drafted by the Boston Red Sox.

Anderson was drafted by the Boston Red Sox in the 10th round of the 1985 amateur draft and made his Major League debut on April 4, 1988. He had been billed as a can't miss prospect, but a lackluster spring resulted in a trade to the Baltimore Orioles with Curt Schilling for Mike Boddicker on July 29. Anderson hit poorly in his first several seasons with Baltimore, neither hitting for average nor power.

Anderson proved himself a capable lead-off man in the 1992 season, scoring 100 runs, hitting 21 homers, driving in 80 runs, stealing 53 bases, and making the all star team, but it was his 1996 season that turned heads. Despite a combined 72 home runs in his first seven Major League seasons, Brady Anderson went into the final game with 49 home runs and second in the league to super slugger Mark McGwire. Anderson hit his 50th home run early in the game off Cy Young winner Pat Hentgen, and in so doing joined an elite club of power hitters. Anderson's 1996 season remains one of the most impressive, and surprising, accomplishments in baseball history. His 50 home runs broke Frank Robinson's record for most home runs in a single season by a Baltimore Oriole. In 1996, Anderson became the only player in Major League history to be in both the 50-20 club and the 20-50 club.

The fan favorite was an all star again in 1997, but he was unable to duplicate his 1996 results over the next several seasons, eventually bowing out of baseball in 2003. His second highest season home run total was 1999 when he hit 24 - less than half of his 1996 total.

In 2004, fellow ex-Oriole Jim Palmer stated in an interview that Anderson's sudden power surge in the mid-90's was attributable to performance enhancers, such as anabolic steroids. Anderson has since flatly denied the allegation and Palmer retracted his statement the following day.

As of 2005, Anderson is one of only two players to have 50+ stolen bases in a season (53 in 1992) and hit 50+ home runs in a season (50 in 1996). Barry Bonds is the only other major league player to have accomplished this.

Anderson now lives in California, where he is raising his daughter Brianna, who was born late in the summer of 2003. He shares joint custody with her mother. Although Anderson had wanted to continue to play baseball longer, he cites wanting to raise his daughter as his main reason for leaving baseball.

In 2003 Brady was inducted into the Baltimore Orioles Hall of Fame.