The moves were announced Wednesday by general manager Mitch Kupchak.
Russell, the second overall pick in the 2015 draft, garnered All-Rookie Second Team honors after finishing last season ranked fourth among rookies in assists (3.3) and steals (1.16) per game and fifth in points (13.2) and 3-point field goal percentage (35.1).
The 20-year-old Russell became the youngest player in NBA history to make 120 or more 3-pointers in a season. Russell was chosen by USA Basketball to compete with the USA Men's Select Team that trained with the Men's National Team in Las Vegas in preparation for the Summer Olympics.
Nance, 23, selected with the 27th pick in the 2015 draft, appeared in 63 games (22 starts) in his rookie season, tallying three double-doubles. He finished third among all rookies in field goal percentage (52.7) and 10th in rebounds per game (5.0). On Jan. 14 at Golden State, Nance recorded a career-high six steals.
Randle, the seventh overall selection in the 2014 draft, was one of only nine players in the NBA last season to average a double-double, and did so in the fewest minutes per game of anyone in that group (11.3 points and 10.2 rebounds in 28.2 minutes per game). He appeared in 81 games (60 starts) in 2015-16, registering 34 double-doubles and one triple-double, finishing the season ranked sixth in the NBA in total rebounds. Randle also was chosen to train with Team USA in preparation for the Rio Olympics.