The 26-year-old defenseman, who was a restricted free agent, avoided a salary arbitration hearing scheduled for Aug. 26.
Zadorov was acquired by the Flames in a trade with the Chicago Blackhawks for a third-round pick in the 2022 NHL Draft on July 28. He scored eight points (one goal, seven assists) in 55 games with the Blackhawks last season and was seventh in the NHL in hits (190).
Selected by the Buffalo Sabres with the No. 16 pick in the 2013 NHL Draft, Zadorov has scored 83 points (23 goals, 60 assists) in 411 regular-season games with the Sabres, Colorado Avalanche and Blackhawks, and eight points (four goals, four assists) in 33 Stanley Cup Playoff games.
The Flames also signed Juuso Valimaki to a two-year, $1.55 million contract. It has an average annual value of $775,000.
The 22-year-old defenseman scored 11 points (two goals, nine assists) in 49 games with the Flames last season and has scored 14 points (three goals, 11 assists) in 73 NHL games, all with Calgary. He was the No. 16 pick in the 2017 NHL Draft.