The gated one-third-acre property they have sold includes a 1922 Mediterranean-style house and a swimming pool.
The 4,600-square-foot home has four bedrooms and four-and-a-half bathrooms.
Public records show the couple bought the Los Feliz house in 2009 for $3.25 million.
The couple own a pied-a-terre in New York and recently bought a Sunset Strip-area compound for $6.5 million.
The new house, built in 1925, boasts nine bathrooms, a guest house, a home cinema and a grotto-style swimming pool.
Perry, 26, started out as a gospel singer before releasing studio albums including One of the Boys and Teenage Dream.
She also stars in the animated film Smurfs, out this week. Brand, 36, starred in the remake of Arthur, released in April, as well as Get Him to the Greek and Forgetting Sarah Marshall.