The 61-year-old, who starred in Twister, True Lies and Aliens, died on Saturday.
A family representative said in a statement: “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.”
Paxton had two children and was married for 30 years.
He appeared in some of the most popular films of the 1980s, from a brief appearance as a blue-haired punk opposite Arnold Schwarzenegger in The Terminator to memorable roles in True Lies, Titanic and Apollo 13.
Major film roles waned in the 2000s but a television career blossomed.
He was nominated for four Golden Globes, including three for his portrayal of polygamist Bill Henrickson opposite Jeanne Tripplehorn and Chloe Sevigny in Big Love.
In 2012 he was nominated for an Emmy for his performance in the civil war drama Hatfields & McCoys, alongside Kevin Costner.