The 33-year-old South Sudanese-born forward,reportedly set to make $2.4 million in his 15th NBA campaign, spent his first 9 1/2 league seasons with the Bulls before being traded to Cleveland.
Deng also joins a Minnesota lineup featuring center Deng Adel, a South Sudanese-born Australian, and Senegalese forward Gorgui Dieng.
Deng has averaged 15.0 points, 6.1 rebounds, 2.3 assists and 1.0 steals a game in 880 appearances over 14 NBA seasons.
With Thibodeau and the Bulls, Deng reached the 2011 Eastern Conference finals and in more than three seasons together from 2010-2014 averages 16.8 points and 6.2 rebounds.
Deng credited Thibodeau for maximizing his talent into All-Star form, reaching the NBA All-Star Game in 2012 and 2013.