Whittington and Robinson are entering their second season in the NBA, while Christmas was a second-round pick in the 2015 NBA draft.
Ashley went undrafted out of Arizona, while Wilson averaged 10.9 points in the NBA D-League last season.
"Jae epitomizes everything that we look for in a Celtic,"Celtics president of basketball operations Danny Ainge said. "His infectious energy on both ends of the court and his versatile skill set enabled him to win over both the coaching staff and our fan base after his acquisition last season."
The trade was first reported on July 7, but the Celtics needed to make various roster moves in order to facilitate the trade.
"On behalf of the entire Golden State Warriors organization, we thank David Lee for his contributions both on and off the court over the last five years," Warriors GM Bob Myers said.
Lee averaged 7.9 points and 5.2 rebounds last season in a reduced role, while Wallace was a non-factor for the Celtics, scoring just 1.1 points in nine minutes.
Haywood averaged 1.6 points and 1.3 rebounds in 22 games for the Cavaliers last season. Miller averaged 2.1 points and 1.8 rebounds per contest in 52 games.
Robinson played for Minnesota and Philadelphia last season.
Jones averaged 4.4 points in 57 games for Cleveland last season.
Butler's deal is for two-years at about $3 million, per Yahoo Sports.
Copeland averaged 6.2 points and 2.2 rebounds in 50 games for the Pacers last season.