Goddard is to make his directorial debut on the picture, while Whedon is to produce it.
The project is the studio's first movie to get the green light from Mary Parent, chairman of the Worldwide Motion Picture Group, MGM, who is rebuilding MGM's theatrical production and marketing divisions, the studio said.
"We couldn't be more excited to green-light our first film with Joss and Drew and for Drew to be making his directorial debut at MGM," Parent said in a statement. "Not surprisingly, 'Cabin' is one of the most original and clever scripts I've ever read. It's a visceral thrill ride and I'll leave it at that."
"This couldn't have turned out better for me," Whedon added. "I'm goofy with the love for this script, and with Drew at the helm and Mary at the ... other part of the helm ... it'll be great!"
Goddard has served as writer/producer on the TV series "Lost" for the past two seasons and wrote the screenplay for "Cloverfield."
Goddard and Whedon first collaborated on the "Buffy the Vampire Slayer" television series, which Whedon created. The team also worked together on the "Buffy" spin-off, "Angel."