Cook, 29, is 6-foot-1 and last played in the NBA with the Cavaliers in 2020-21, appearing in seven games. He has also spent time with the Lakers, Warriors, Pelicans and Mavericks, winning two championships along the way.
Last season, he played for the Stockton Kings, Sacramento’s G League affiliate.
Bazemore, 33, is 6-4 and spent last season with the Lakers, appearing in 39 games. He spent the season before last with the Warriors.
This isn’t his first run with Sacramento, having played there in 2019-20. He has also spent five years with the Hawks.
Bazemore is the second former Laker to sign with the Kings this offseason, joining guard Malik Monk.
Last season, Bazemore averaged 3.4 points on 32 percent shooting, his lowest numbers since his rookie year of 2012-13.
Both players are believed to have received non-guaranteed deals for training camp.