According to The Sun, the singer jokingly refers to her as "sis" and the royal has an open invitation to visit him whenever she likes.
A source said: "Robbie gets on really well with Beatrice. He treats her like a little sister and looks after her. It's really sweet."
The insider added that the Take That star is also very close with Ferguson, who has visited him and his wife Ayda Field on many occasions.
"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," the source added.
The two became friends when Ferguson shared a Caribbean holiday with Williams in January.
Williams is tipped to stay with Take That for their next studio album.
Princess Beatrice is expected to attend the royal wedding on April 29, while her mother is reportedly not invited.