The "Umbrella" singer is said to be smitten with Shia - who is currently filming the fourth "Indiana Jones" movie with Harrison Ford - and the couple are believed to have been an item for a couple of months.
A source is quoted by online gossip columnist Perez Hilton as saying: "Shia and Rihanna are officially a couple. It's the talk of the 'Indiana Jones' set."
The couple, who are said to be taking things slowly, were seen having a romantic meal in Beverly Hills restaurant Kate Mantilini on Tuesday (August 28, 2007).
Rihanna is reportedly planning to make her first public appearance with the "Transformers" actor at the MTV Video Music Awards in Las Vegas later this month.
The 19-year-old singer recently revealed Jay-Z screens all her dates, and her protective mentor must give his approval before they are allowed to date her.
She said: "I just found out from a mutual friend that guys will talk to Jay first before they try to approach me."
"He's very protective. Jay has my best interests in mind. If it's a good guy I know Jay won't shut him down. But if he's not, Jay will be like, 'No, no, no.'"
Rihanna - who Jay-Z discovered and signed to his Def Jam record label - also revealed the rapper never tells her who failed to make the cut.
She added: "He actually never tells me. I have no clue who they are and I guess I'll never know."
