The 27-year-old pop star has been spotted out and about with the rapper several times this week and it's claimed they are now an item.
A source told E! News: "Travis and Rihanna are dating, officially. It's already very serious. He's very into her."
The news comes just two days after Rihanna was spotting kissing Travis, 23, at a New York Fashion Week party on Friday night.
Rihanna and her new beau flaunted their burgeoning romance as they partied at the New York Edition Hotel, dancing together and kissing in front of guests.
Meanwhile, it's thought Travis, who co-wrote Rihanna's track 'Bitch Better Have My Money', has already won over the singer's friends.
An insider said: "Rihanna likes Travis a lot and hopes it develops into something more. All of her friends think he is gonna be the keeper."
As well as the Fashion Week party, Rihanna was spotted at Travis' concert earlier this week and the pair attended a private after party together later in the evening.
A source said: "It's true, they were totally together. They were all over each other. It was very clear they were together."