Rubio averaged 10.6 points, 8.2 assists and 4.2 rebounds per game last season. He finished as runner-up in the NBA's Rookie of the Year voting and finished sixth in the league, and first among rookies, in assists last season. The second-year guard from Spain is recovering from surgery in March to repair torn ligaments in his left knee.
Williams appeared in all 66 games for the Timberwolves as a rookie, averaging 8.8 points and 4.7 rebounds per game. The second overall pick in the 2011 NBA draft out of Arizona finished fifth among rookies in rebounding and seventh in scoring last season.
The Timberwolves announced the move on Tuesday.