The Pru, which said the deal plugs a gap in its range of long-term savings products, is making a cash offer of pounds 25 a share, a premium of 40 per cent to Wednesday's closing share price.
M&G, which has a customer base of 730,000 and some pounds 18.5bn funds under management, will operate as an autonomous unit within the Pru, giving the group a unit trust business to stand alongside its growing stable of retail financial brands including Scottish Amicable and Egg.
Sir Peter Davis, the Pru chief executive, said: "The combination of the Prudential and M&G creates leading market positions in the UK retail and investment product sectors."
Analysts said that the Pru needed to expand its unit trust business dramatically in response to the growing shift out of traditional life insurance and savings, a process that is likely to accelerate as a result of the Government's attempts to encourage more people to save.
M&G will take on the running of the Pru's existing unit trusts' stable while the Pru will take over M&G's institutional client base. There were also hints that Michael McLintock, M&G's youthful chief executive, is being lined up as a potential long-term successor to Sir Peter, who is 58 this year.
M&G's largest shareholder, the Esmee Fairbairn Charitable Trust, has agreed to sell its entire 33.3 per cent, conditional on the deal receiving the necessary regulatory approval, as have M&G's directors who own a further 0.44 per cent.
Rod Kent, the chairman of M&G, said the group had been courted over the past 18 months by a number of potential buyers including the Halifax, Britain's largest mortgage bank, but recently went back to the Pru. The Pru had originally approached M&G a year ago after deciding that it was the partner that made the most sense. "This is a good strategic fit but also a good cultural fit," Mr Kent said.
Analysts said the Pru had had to pay a pretty full price in return for having an exclusive run at M&G. But, having done so, it was now unlikely to see itself trumped by a higher bid.
Richard Burden at Goldman Sachs said: "This is a knock-out bid. But banks and insurance companies are not going cheap. This deal is strategically right."
The Pru is paying the equivalent of 10 per cent of assets under management. That compares with the 3 per cent paid by Merrill Lynch to buy Mercury Asset Management last year.
Jonathan Bloomer, the Pru's finance director, said: "The price is full but fair. It reflects firstly the fact that the deal has a degree of certainty, and second the scarcity value of M&G, which until yesterday was the only independently quoted asset manager in the UK of any real size.
"After having a couple of rough years, the changes Michael McLintock has made are starting to pay off."
He expects cost savings of pounds 10m a year, mainly as a result of eliminating the costs associated with M&G's plc status and from pooling resources.