Premier Foods, which bought the Ambrosia dessert brand from Unilever last year, also owns HP Sauce, Typhoo and Branston Pickle.
Angel Delight, Bird's Custard and Dream Topping generated sales of £37m last year and profits of £9.9m.
The three brands are all well known to British consumers, but lack the international profile that provides US giant Kraft with economies of scale in sales and marketing.
It is understood that Kraft wanted to offload the brands because of their dated image and lack of convenience or healthy appeal element, which is seen as more fitting with modern lifestyles and changing tastes.
Robert Schofield, Premier chief executive, said: "The Bird's business with its high brand recognition is a perfect fit with our Ambrosia and other dessert brands.
"It will extend our product range in the desserts category and enhance our position as one of the UK's leading suppliers of ambient grocery products."
Despite the changing attitudes, Bird's Custard remains the top seller in its market and comes with a 167-year heritage, having been developed in 1837 by chemist Alfred Bird.
Dream Topping and Angel Delight, which were launched in the 1960s, were also part of the Bird's range.
Angel Delight, which is made by mixing with milk and then chilling in the fridge, became a favourite with children in the 1960s and 1970s.
Kraft bought the brand from General Foods, which last relaunched it in 1984.
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