The England rugby star reportedly suggested to Brook that the pair should live together earlier this year when the couple were on holiday in the Caribbean.
A source told The Sun: "They're very much in love and felt it was right to take the next step. Even though Danny is eight years younger, he feels Kelly is the one and wants to settle down.
"They're enjoying the first few weeks of excitement you have when you move in with someone."
It is believed that Brook and Cipriani are renting a home in South West London.
The insider added: "They both felt it would be best to rent and see how they get along before buying somewhere. Danny's always lived at home and it was a bit of a wrench to leave his mum - but he knew he had to move out sooner or later."