Permira outbid CapVest, a rival private equity firm that owns FoodVest, the holding company behind Findus frozen foods in Norway, Sweden and France, as well as the UK's Young's Bluecrest Seafood.
Unilever took the decision to sell off Birds Eye last autumn, after failing to expand the business and revive its flagging image.
Although Birds Eye is still a profitable part of Unilever's portfolio, with sales of its vegetable and fish lines increasing, its frozen meals and frozen chicken products have not performed as well and have been hit by increasing consumer concerns about healthy eating.
The deal ends a 63-year association between Unilever and the Birds Eye brand, famous for its Captain Birds Eye advertising campaigns.
The business, which also includes the Iglo brand, operates in 10 European countries, including the UK, and employs about 3,500 people.
Unilever will retain its Walls ice cream business, as well as its Italian frozen-food division. The Italian business is understood to have stronger growth potential than the rest of Europe.
The deal, overseen by investment bank Goldman Sachs, is due to be signed by the end of today, but is not totally final and it is still possible that another investment group could join the running if Permira fails to close the deal.
CapVest was seen as frontrunner to buy the business after boosting its chances by recruiting two other buyout firms, Kohlberg Kravis Roberts and CVC Capital, to its bid, but both dropped out. It also lost Martin Glenn, the former head of PepsiCo, it had hired to head the bid.
City analysts believe that CapVest will now try and offload its own FoodVest business for £800m-£900m, with Permira a possible buyer. Those involved in the Birds Eye deal say acquiring FoodVest is a logical next step for Permira, a move that will create a frozen food business worth £2bn.
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