The pair were spotted cruising around in his car in Los Feliz earlier this week, and now sources close to the Presley family have confirmed their romance to The Mirror.
“The relationship is very new but they’ve got close quickly and are hanging out together a lot, enjoying each other's company," they said.
Another added to the MailOnline that he is impressed by her rock status.
"They're inseparable. Rob loves the fact that Riley is Elvis's granddaughter - that's true Rock'n'Roll royalty in his eyes," they said.
Awkwardly, Riley starred with Rob's ex Kristen in the 2010 film 'The Runaways', and K-Stew is said to be devastated about their blossoming romance.
The Mail source added: "Kristen feels that she acted as mentor to Riley on her first film The Runaways, introduced her to Rob and encouraged her to make a career of acting.
"Kristen is emotionally volatile at best of times and flew off the handle when she found out about Rob's liaison with Riley. She's told Rob via friends she feels violated."