Kopelman proposed to the Never Been Kissed actress over the Christmas holidays while vacationing in Sun Valley, Idaho.
"It's really positive. I'm super happy. As I've gotten older, I've really wanted to find more balance and calm," Barrymore told InStyle in an interview conducted shortly before the couple's engagement.
She also said that Kopelman gets along well with her friends, adding that they take holidays together and often go on group outings.
Barrymore has been married twice previously, to Tom Green between 1999 and 2001 and to Jeremy Thomas for a short time in 1994.
It was reported in October that Barrymore was "yearning to get married and have kids".
In November, she was named Hollywood's Most Overpaid Actor by Forbes, topping a list which also included Eddie Murphy, Will Ferrell and Reese Witherspoon.
Watch the trailer for Drew Barrymore's directorial debut Whip It! below: