The 25-year-old performer's publicist, Eddie Michaels, said she had become engaged to Green, 28, in the last 10 days.
Barrymore, who comes from an acting family, stars in the forthcoming film based on the TV series Charlie's Angels, which also features Cameron Diaz and Lucy Liu.
A child performer from the age of eleven months, she made her debut in a 1976 dog food ad and hit worldwide fame at seven with her performance as Gertie in her godfather Steven Spielberg's film ET.
Drug abuse
But she is also remembered for her dramatic descent into alcohol and drug abuse.
By the age of 13 she was in a rehabilitation clinic, and then tried to run away to Hawaii with a credit card belonging to her mother - also her manager. Spielberg commented that Barrymore was "13 going on 29". The following year, she attempted suicide.
When she was 15, the so-called "wild child" became legally separated from her parents.
During the 1990s her career - and her lifestyle - gradually recovered. She founded her own production company in 1994 and took roles in Scream and Woody Allen's Everyone Says I Love You in 1996.
Cancer surgery
Tom Green's MTV show, featuring crude humour and elaborate stunts, became an instant success when it started in January 1999. He started out as a comedian and radio DJ in his native Ottawa, Canada.
Some thought his jokes had gone too far when he announced he was battling testicular cancer earlier this year.
But he underwent surgery in March, with Barrymore at his side during the ordeal.
He recovered and returned to work, setting up a charity to raise funds for cancer research - typically called the Tom Green's Nuts Cancer Fund.
Green makes a cameo appearance alongside Barrymore in Charlie's Angels, due for release in the US and UK in November.
He will be Barrymore's second husband - she was briefly married to British bar owner Jeremy Thomas in 1994.