The art consultant popped the question during a winter break in Sun Valley, Idaho according to Us Weekly magazine.
The Charlie's Angels star began dating Kopelman last year (11) after splitting from longtime on/off boyfriend Justin Long.
Sources tell the magazine that Barrymore and her new fiance dated briefly in 2010.
The insider tells the publication, "He's madly in love and knows she's the one."
Barrymore's previous two marriages to bar owner Jeremy Thomas in 1994 and comedian Tom Green in 2001 were short-lived - both lasted less than five months.
The actress also had a long romance with The Strokes drummer Fabrizio Moretti.
The movie star has yet to confirm the engagement news.