The couple has set their wedding date in June, reported Us Weekly.
Barrymore picked a summer wedding "because she wants to get married before the baby comes, but doesn't want to be huge," said a source close to the actress.
The insider confirmed that Barrymore recently visited Paris in search of the perfect gown. She is said to have chosen a dress by Chanel, where Kopelman's father used to serve as head of the fashion house.
"Drew met with his staff and had the first of many fittings," the source told Us Weekly. "She'll likely put [Kopelman's] nieces and nephew in the wedding party."
While rumors of her engagement were confirmed, a new round of gossip has speculated that Barrymore is pregnant. The couple has not commented on the pregnancy reports.