The Brokeback Mountain actor moved into Witherspoon's Los Angeles home last month and according to Star, the actress insisted on composing a series of strict rules for her boyfriend.
An insider said: "Reese believes in wide-open communication, and she discussed at length with him what is best for her household.
"Some of [the things she insists on] are run-of-the-mill. He has to take off his shoes when he's in the house; trash must be taken out when the can is three-quarters full; and no feet on the coffee table."
The source added that Witherspoon has clamped down on Gyllenhaal's swearing: "Jake used to swear like a sailor, but not anymore. If he does, he has to apologise."