The Marlins are expected to officially announce the remarkable deal - believed to include an opt-out clause after six years - on Wednesday.
Jeffrey Loria, the team's owner, was delighted the parties had come to an agreement.
"This is a landmark day," he told MLB.com.
"I'm happy for the city. I'm happy for him. And I'm thrilled for baseball. We have a player who is committed to us, and we've committed to him for the life of his career."
Stanton finished the MLB season with a .288 batting average, with 37 home runs and 105 RBIs as the National League MVP runner-up.