She posed for pictures in the nine-bedroom, 12-bathroom Bel Air house and said she was "just so happy" to be there.
She told Hello! Magazine: "The sun is shining, my sister is close by... I just feel as though 2013 is going to be the best year ever."
The house, which also includes a bar, a gym and a private cinema, is not her main home though -- she is about to collect the keys to her multimillion-pound refurbished west London house.
Ecclestone, daughter of Formula One boss Bernie, said: "I'm very excited about it: it's a new beginning."
She is also on the lookout for a new man and said she now knows what she wants in a man.
She said: "Without trust, you have nothing: trust is so important. Oh, and he has to love his mum. If he can't love his mother, how can he love anyone else?"