Watson is a graduate of Washington High School in Kansas City, Kansas. In his senior year of high school he averaged 23.4 points, 8.3 assists and 14 rebounds per game.
Watson was a starter in college at UCLA, at one point playing alongside future NBA All-Star Baron Davis. They were the first two freshmen to start at UCLA since the 1979 season. A four-year starter, Watson started the most consecutive games in the history of UCLA basketball. As a senior, He averaged 14.7 points (2nd on the team, 9th in the pac-10), 5.2 assists, (1st on the team, 2nd most in the pac-10) 3.7 rebounds, 0.3 blocks, and 1.9 steals (most in the pac-10, most on the team) per game. He earned All-Pac-10 First Team Honors.
Watson was selected in the second round (39th overall) by the SuperSonics in the 2001 NBA draft. In the 2007–08 NBA season, Watson averaged 10.7 points and 6.8 assists with the Sonics. On February 6, 2008, Watson recorded his first-ever triple-double in a game against the Sacramento Kings. Watson logged 23 points, 10 rebounds and 10 assists in 32 minutes. It was Seattle's first triple-double since Ray Allen registered one on January 28, 2004, against the Los Angeles Lakers.
On July 17, 2009, Watson was waived by the Thunder. He signed a one-year deal with the Indiana Pacers on July 28, 2009.
On October 2, 2014, Watson was hired as an assistant coach by the Austin Spurs of the NBA D-League, effectively ending his 13-year playing career. He joined the Phoenix Suns as their new assistant coach on July 30, 2015. However, after a poor start to the 2015-16 season, the Suns fired coach Jeff Hornacek and replaced him with Watson as the interim head coach for the rest of the season.