Yelchin will be the son of Gibson's and Foster's characters. Gibson plays a severely depressed man whose only happiness is wearing a beaver hand-puppet. Foster plays his wife, and Yelchin's character wants them to get a divorce.
The script was written by Kyle Killen. Foster initially came on to the project and then brought it to Gibson. The two worked together in 1994's Maverick.
Jennifer Lawrence has also been added to this project.
Summit Entertainment bought The Beaver last month and hopes to release the film in 2010 or early 2011.