Meanwhile, 29-year-old Ben had previously gushed about his actress girlfriend with a picture he posted on Instagram on New Year's Day.
He wrote: "Sometimes in life you get extremely lucky, and the smartest, funniest, most beautiful woman comes along when you least expect it. Here's to what adventures 2016 brings!"
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It remains to be seen whether Amy will make her red carpet debut with Ben at Sunday's Golden Globe Awards, where she is nominated for her role in movie Trainwreck.
But sources close to the actress said she is enjoying every second of her new romance.
A source told People: "He makes her so, so happy. She calls him her boyfriend and says he constantly tells her how pretty, sexy and perfect she is.
"She feels like she hit the jackpot."
-Bang! Showbiz