The 25-year-old forward was a restricted free agent.
Kiviranta scored 11 points (six goals, five assists) and was limited to 26 games last season because of a lower-body injury.
"Joel has developed into a very reliable player who can play various roles throughout the lineup," Stars general manager Jim Nill said. "His competitiveness, and ability to play in all situations, has made him an important member of our forward group."
Signed by Dallas as a free agent May 31, 2019, Kiviranta has scored 12 points (seven goals, five assists) in 37 regular-season games and six points (five goals, one assist) in 14 Stanley Cup Playoff games.
Kiviranta scored a hat trick, including the game-winning goal in overtime in Game 7 of the Western Conference Second Round against the Colorado Avalanche in 2020. He scored one goal in the Stanley Cup Final, which the Stars lost to the Tampa Bay Lightning in six games.
