British newspaper the Daily Mirror has reportedly obtained titles deeds which prove she has purchased the pad.
Despite rumours that she has reunited with her ex-husband Ashley Cole, 30, the documents list 28-year-old Geordie Cole as an 'unmarried woman'.
A source told the publication: 'Cheryl bought the apartment back in March when she was still on the US X Factor. But she loves Los Angeles and when the TV show didn't work out decided not to renege on her offer but use it as a base for her music career. If things go well with Ashley, the hope is that they can both use it as a base out there.
'Ashley has a club deal with Jay-Z so he'll be spending more and more time in the States anyway. It makes perfect sense.'
The star, who has been in Los Angeles this week, is said to be spending the weekend with her footballer ex.
The source added: 'Ashley's mum Sue and Cheryl's mum Joan are invited and it'll be a lovely, quiet family do before Ashley goes off next week on pre-season training.'