Demi Moore

The 50-year-old actress - who has three daughters with the 'Die Hard' actor, Rumer, 24, Scout, 21, and 18-year-old Tallulah - is "really happy" that the star, 58, and his wife Emma Hemming have purchased a unit near hers inside the luxurious San Remo apartment block.

A source told Life & Style magazine: "Bruce and his wife, Emma, just moved in. Demi is really happy. They both love their kids and living in the same building will give them a lot of privacy."

The former couple are still on great terms and Bruce has supported Demi since her split from Ashton Kutcher.

The insider added: "Bruce has been her shoulder to lean on through the divorce with Ashton."

Earlier this month, the 'Ghost' actress missed daughter Scout's graduation from Brown University in Providence, Rhode Island.

Bruce and wife Emma attended the joyous occasion along with Rumer and Tallulah, but Demi was conspicuously absent.

A source said: "The buzz was that Demi was supposed to come in, but everyone was wondering where she was. She was nowhere to be seen all weekend, but everyone seemed to be having a perfectly good time without her."