The Ducks announced the deal Friday.
The 6-foot-6 Steckel has scored 73 points in 398 games over eight NHL seasons with Washington, New Jersey and the Maple Leafs. He played for the Capitals under Bruce Boudreau, now the Ducks' coach.
Steckel excels on faceoffs and penalty killing, two areas of need for Anaheim.
The Maple Leafs needed to clear a roster spot with Joffrey Lupul returning from a broken right arm. Toronto acquired Steckel from the Devils in October 2011.
Lasch played 19 games for the Ducks' AHL affiliate in Norfolk this season, and most recently played for Vaxjo in the Swedish Elite League.