The cash offer, which is pitched at 150p a share, trumps an earlier indicative bid for Paramount from its management, who had been preparing to offer around 135p a share.
Paramount shares jumped 25.5p to 145.5p as Greencore revealed it has irrevocable acceptances from shareholders representing 53.1 per cent of Paramount's share capital. It is thought that the Kent family, who founded the group, are among the shareholders accepting the bid.
The price represents a multiple of 13.5 times Paramount's earnings per share for the year to December 1997.
Kevin O'Sullivan, Greencore's finance director, said he expected Paramount's existing management to stay on and develop the business. He added that the pizza market was expanding at about 10 per cent a year.
Paramount, which changed its name from Canadian Pizza last year, sells pizza crusts and toppings to supermarkets and health food shops. It also makes sauces, dips and marinades.
Greencore said Paramount was an ideal bolt-on for its existing businesses. Greencore's Kears subsidiary is one of the largest baking groups in the UK.
It added that Paramount's sauces and dips business could be integrated with Greencore's Erin subsidiary, which makes soups and sauces in Ireland.