Matt Bellamy and Kate Hudson got engaged in April
The Hollywood actress and the 33-year-old Muse frontman plan to move into their new home just before the birth of their baby, due this summer.
The 7-bed pad, in the Pacific Palisades area of the city, sits just down the road from where Kate's actress mum Goldie Hawn, 65, and her partner Kurt Russell, 60, are based.
Once Kate - who's already mum to Ryder, 7, with ex-husband Chris Robinson - has given birth, she doesn't expect to be home that much.
Because of his busy touring schedule and Kate's successful acting career, the family plan to live life on the move.
'We travel, we'll be where we are. We don't really know where that is,' Kate, 32, told the Daily Record recently.
'We obviously know London and LA is where we live, but between his job and my job, a travelling family is just what it is.'