Pinewood Shepperton - home to the James Bond and Harry Potter films - has agreed to be bought by Peel Holdings.
The deal comes after Peel, which is chaired by billionaire property tycoon John Whittaker, raised its offer to £96.1m from £87.8m.
The bid for the 75-year-old film studio has been recommended unanimously by the boards of both companies.
Last week, Mohamed Al Fayed said that he was considering making a cash bid for Pinewood.
But at the time the Egyptian businessman added: "There can be no certainty that an offer will be forthcoming".
Peel already owns a 29.78% stake in Pinewood and, under the terms of the deal, has offered 200p for each share in the studio.
Its bid has also won the support of the Crystal Amber fund, which owns 27% of Pinewood.
Last month, Pinewood unveiled a 31% rise in pre-tax profits to £5.8m, and said it was looking to the future with "confidence" despite a poor economic climate.
Pinewood has studios in Buckinghamshire, and at Shepperton and Teddington in Middlesex.
"Peel represents a long-term strategic partner for Pinewood in continuing to grow and develop the business," said Mr Whittaker.
Peel recently sold Manchester's Trafford Centre to Capital Shopping Centres for £1.6bn.