Gibson will take on the role of a depressed man who wears a beaver puppet on his hand believing it to be real. Foster, who appeared with Gibson in 1994's Maverick, will also star in the film as the man's wife.
Steve Carell and Jim Carrey had previously been touted for the lead role. Kyle Killen's Beaver was named the top script in last year's Blacklist, a list compiled by Hollywood agents, executives and producers to find the best screenplay of the year.
The Beaver will be Foster's first directorial venture since 1995's Home For The Holidays. She also helmed Little Man Tate in 1991 and has been working on period drama Flora Plum for several years with a view to directing.