James Goldstein says he hopes the building will encourage people to build more architecturally creative homes.
The donation will eventually see the house officially opened to the public.
The house features in a scene of the 1998 movie when the main character The Dude, played by Jeff Bridges, pays a visit to pornographer Jackie Treehorn.
The museum will inherit the house's gardens, art pieces and fashion collection in addition to the building itself.
"Los Angeles should represent a city that's contemporary and moving into the future," Goldstein said.
"I want people to build houses in a way that haven't been done before, that are moving into the future instead of the past, so I hope my house is an inspiration for that kind."
The house - officially known as the Sheats Goldstein residence - featured prominently in the Coen brothers' film which co-starred Julianne Moore and John Goodman.
Since then, the residence has also been seen in Charlie's Angels: Full Throttle and as a back-drop in high-fashion photo shoots.
Features of the house include huge windows with views of the LA skyline, a swimming pool, tropical gardens and a roof, with hundreds of small skylights, which curves into the ground.
The house was originally built by John Lautner in the 1960s but Goldstein has been enhancing it over the subsequent decades.
The owner of a luxury house owned by a fictional porn baron in The Big Lebowski is donating it to the Los Angeles County Museum of Art.