He played college football for Washington State Cougars, winning Pac-10 Offensive Player of the Year as a junior, and was selected by the Patriots first overall in the 1993 NFL draft.

He was unable to regain his starting position for the remainder of the season due to Brady's success, which led to the Patriots winning their first championship in Super Bowl XXXVI and began a dynasty for the franchise.

He then spent three seasons with the Buffalo Bills, where he made a fourth Pro Bowl appearance, and his final two with the Dallas Cowboys.

After gaining the starting job at the end of the 1990 season as a true freshman (joined later by Jeff Tuel and Jayden de Laura as the only three in school history), he quickly became the face of the Cougars' offense.

[15] Bledsoe led a comeback victory in which the Patriots won, 26–20, in overtime, as he set single-game records in pass completions (45) and attempts (70).

[16][17] The win sparked the beginning of a new age for the Patriots, as they rallied behind Bledsoe and won their final six games to finish with a 10–6 record and capture the wild card spot.

[21][22] Following the difficult 1995 season, Bledsoe turned it around in 1996, ranking among the top passers in the league with the help of wide receiver Terry Glenn, pushing the Patriots to reach the playoffs again and winning the AFC championship over the Jacksonville Jaguars, 20–6.

The Patriots lost in the Divisional Round to the Pittsburgh Steelers;[28] however, Bledsoe built a career-high 87.7 passer rating, passed for 3,706 yards, tossed 28 touchdowns, and earned his third Pro Bowl invitation.

[32] He completed these come-from-behind efforts while playing with a broken index finger on his throwing hand, an injury that would later sideline him for the postseason.

[37] During the second game of the 2001 season on September 23, Bledsoe was racing toward the sideline on third-and-10 when New York Jets linebacker Mo Lewis leveled him with a hard, but clean hit.

[42] Bledsoe, starting from the Steelers' 40-yard line, capped a scoring drive with an 11-yard touchdown pass to David Patten to give the Patriots a 14–3 lead, as well as all of the momentum going into halftime.

Bledsoe later drove New England into Steelers territory to set up a 50-yard kick to seal the game, however Vinatieri missed and the ball went back to Pittsburgh.

[2] Brady started as quarterback as the Patriots won Super Bowl XXXVI, with kicker Adam Vinatieri hitting a game-winning 48-yard field goal as time expired.

[45] Patriots fans appreciated Bledsoe's lengthy tenure and his role in improving the team, and cheered him in each of his three returns to New England as a visiting player.

However, a flurry of injuries stymied the Bills offense; they failed to score a touchdown in three consecutive games en route to a 6–10 season.

[54] When Bledsoe later signed to the Dallas Cowboys, he expressed bitterness with the Bills for the move, stating "I can't wait to go home and dress my kids in little stars and get rid of the other team's [Buffalo's] stuff.

[56] During his tenure with the Cowboys, he threw for over 3,000 yards in a season for the ninth time in his career, tying Warren Moon for fourth in NFL history.

[57] Though the team ultimately failed to reach the playoffs, Bledsoe led them to a 9–7 record, an improvement over the 6–10 mark that Vinny Testaverde had finished with in 2004.

[67] Bledsoe beat former head coach Bill Parcells and defensive lineman Houston Antwine in a fan vote.

[68] In January 2018, Bledsoe was named honorary captain of the New England Patriots as they hosted the Jacksonville Jaguars in the AFC Championship Game.

"[2][3] The Patriots defeated the Jaguars 24–20 to advance to their tenth Super Bowl appearance and Bledsoe presented the Lamar Hunt Trophy to Kraft.

The only time Drew played a whole season of football without ever starting at quarterback was in seventh grade at Pioneer Junior High.

In high school, with his father as his coach, he won numerous awards, including selection to the Western 100 and Washington State Player of the Year.

[77] After the 2014 vintage, Figgins left Doubleback and handed his interest in the business to his protege Josh McDaniels (not related to the Patriots assistant coach of the same name).

[82] In 2021, Bledsoe purchased an 80-acre (32 ha) property in Oregon's Eola-Amity Hills AVA with his business partner and winemaker Josh McDaniels.