The Stars gave up a conditional draft pick in 2008 for Green, who had 17 goals and 26 assists in 50 games with the Hannover Scorpions of the German Elite League last season.
Green played for the Rangers and Florida Panthers before the 2004 lockout. He had one goal and three assists in 24 games.
The 32-year-old Lehtinen had career highs last season in goals (33) and power-play goals (14), and he led the Stars with six game-winning goals, tying a career best. He helped Finland win an Olympic silver medal.
The Stars also signed winger Niklas Hagman to a two-year contract. Acquired in a midseason trade with Florida, Hagman had eight goals and 13 assists in 84 games with the Panthers and Stars.