The statement read: "It is with heavy hearts we share the news that Bill Paxton has passed away due to complications from surgery.
"A loving husband and father, Bill began his career in Hollywood working on films in the art department and went on to have an illustrious career spanning four decades as a beloved and prolific actor and filmmaker.
"Bill's passion for the arts was felt by all who knew him, and his warmth and tireless energy were undeniable. We ask to please respect the family's wish for privacy as they mourn the loss of their adored husband and father."
A number of stars have taken to social media to pay tribute to the actor, including his True Lies co-star Jamie Lee Curtis.
She wrote: "Nooooo. Bill Paxton is gone. Such a funny, talented, loving human. Louise & the children & family my [love] & support 2 u. #truelies (sic)"
Nooooo. Bill Paxton is gone. Such a funny, talented, loving human. Louise & the children & family my ❤& support 2 u. #trueliespic.twitter.com/d4zleWdOrR
Meanwhile, Breaking Bad actor Aaron Paul remembered one of the "greatest guys" he'd ever met.
He wrote: "Bill Paxton was hands down one of the greatest guys that I have ever met. I feel lucky to have called him my friend. Bill, I love you. RIP. (sic)"
Lou Diamond Phillips posted: "I am stunned & saddened at the passing of Bill Paxton. I just worked with him recently. A warm and beautiful soul and a talented actor. RIP (sic)"
I am stunned & saddened at the passing of Bill Paxton. I just worked with him recently. A warm and beautiful soul and a talented actor. RIP
Bill also starred in TV drama Big Love and the small screen adaptation of Training Day, and he won an Emmy award for his performance in historical TV miniseries Hatfields & McCoys.