Tutor and his partners put down a nonrefundable deposit of $40 million to Disney on Thursday.
Disney had been looking to sell Miramax amid a studio overhaul because it no longer resonated with its other family-centric studio units such as Pixar and Marvel.
Miramax's Oscar-laden film library is full of prestigious films such as "My Left Foot" (1989), "Pulp Fiction" (1994) and "Good Will Hunting" (1997).
The label was founded in 1979 by Harvey and Bob Weinstein, who named it after their parents, Miriam and Max. It was sold to Disney for $80 million in 1993, and the brothers stayed on as managers.
The Weinsteins' recent bid to buy Miramax with the financial backing of supermarket magnate Ron Burkle was halted after Burkle cut the offer price to about $565 million from $625 million.
Disney is the parent company of ABC 30.