"Crazy, beautiful things went down over the holidays and of course quality time with the family was long over due," wrote the 30-year-old former Real World: San Diego cast member.
Sources told E! News that the couple, who spent the New Year's holiday in Turks and Caicos, are recently engaged.
"I couldn't help myself. Shameless #selfie so happy to be in paradise with my baby!!!!" she captioned an Instagram photo.
Greenberg, 30, first made a name for himself on One Tree Hill and starred in HBO's short-lived series How to Make it in America. He'll also star in an upcoming Lance Armstrong biopic.
[E! News, New York Daily News]