The 35-year-old forward was an unrestricted free agent. He scored 17 points (five goals, 12 assists) in 31 regular-season games with the Blues last season, and two points (one goal, one assist) in four Stanley Cup Playoff games.
Signed by the Toronto Maple Leafs as a free agent April 3, 2009, Bozak has scored 449 points (167 goals, 282 assists) in 764 regular-season games for the Blues and Maple Leafs, and 27 points (11 goals, 16 assists) in 56 playoff games. He won the Stanley Cup with the Blues in 2019.
St. Louis previously agreed to terms with forwards Zach Sanford (one year, $2 million) on Aug. 4, Jordan Kyrou (two years, $5.6 million) on Aug. 3 and Pavel Buchnevich (four years, $23.2 million) on July 27. Forward Brandon Saad signed a five-year, $22.5 million contract on July 29, and forward Ivan Barbashev agreed to a two-year, $4.5 million contract on July 30.
Forward Robert Thomas is the remaining unsigned restricted free agent on the Blues roster.
The Blues begin the regular season at the Colorado Avalanche on Oct. 16.