The 33-year-old January, who has been named to the WNBA's All-Defensive team six times, averaged 6.5 points and 3.3 assists in 33 games for Phoenix last season.
Williams, 25, averaged 13.2 points in helping Connecticut reach the Finals last season.
''What fans will love the most about Courtney is the joy and passion they will see every time she steps out on the court,'' Atlanta coach Nicki Collen said.
Connecticut Sun coach and general manager Curt Miller made it clear that Williams wanted the trade.
''Unfortunately, despite our best efforts and all the loyalty and support we've shown Courtney over the last four seasons, it became clear she no longer wanted to return to Connecticut,'' he said. ''I will look back fondly on the memories we created together, but my focus as always is with the players that have a burning desire to help the Connecticut Sun hang the franchise's first championship banner.''
Williams disputed her former coach's take posting on Instagram that she ''Never intended nor wanted to leave CT and I hope the Connecticut fans and my teammates really understand that. Thank you to the fans and my teammates for really accepting a kid like me and my different ways of doing things. Y'all are really something special and I love y'all forever!''
Breland, a shot blocking specialist, 32 on Sunday, averaged 7.5 points and 6.0 rebounds last season.
Coffee, 24, averaged 5 points and 2.8 rebounds in 2019 for Atlanta.