Among the high-profile names to add their congratulations in the comments were Josh Brolin and Rosanna Arquette.
Penn was previously married to Madonna and Robin Wright and has been linked to Charlize Theron, Susan Sarandon and Downton Abbey star Elizabeth McGovern. He has two children with Wright, born in 1991 and 1993.
George, born in Sydney in 1992, is the actor daughter of American actor Vincent D'Onofrio (Men in Black, Law & Order: Criminal Intent) and Italian-Australian actor Greta Scacchi (Palm Beach).
George has credits in TV movie "Mother, May I Sleep with Danger?" and Peter Jackson-produced box office flop "Mortal Engines", and featured opposite her mother in a stage production of Anton Chekhov's "The Seagull" in Perth.
Penn was long list of career-defining performances in films such as "Milk", "Carlito's Way", "Mystic River" and "Dead Man Walking", and has also directed movies including "Into The Wild."
He is also known for his activism, especially for his advocacy for Haiti.
According to People magazine, Penn and George have shared interests in activism and philanthropy. George helped organise an fundraiser earlier this year in support of wildlife relief after Australia's devastating bushfires.