He reportedly proposed with a pink, gold diamond ring over the holidays in New York City before the pair jetted to London for New Year's.
The news comes approximately five months after Roberts, 22, was arrested for domestic violence against Peters, 26. He decided not to press charges and she was released hours later.
The couple began dating in 2012. In addition to their roles on American Horror Story: Coven, Roberts most recently starred in We're the Millers, and Peters will next appear in X-Men: Days of Future Past.