The Take That star, 37, lives in a £10million home in Beverly Hills and Beatrice, 22, met him when her mum took her there for a visit.
It's claimed she has now been given an invitation to visit him at any time and he has even been calling her 'sis' as a joke.
A source said to UK newspaper The Sun: 'Robbie gets on really well with Beatrice. He treats her like a little sister and looks after her. It's really sweet.'
Beatrice's mum Fergie, 51, is a good friend of the singer's and regularly visits him there.
The source added: 'A few of Robbie's football pals were round the other week and Fergie was just wandering about in her robe. She came and said hello and was really charming.'