The consortium placed a binding offer for the division, which includes Orangina, Oasis and Schweppes brands, and has been officially up for sale since the beginning of September.
Todd Stitzer, Cadbury Schweppes' chief executive, said he was delighted to receive such a firm offer in such a short time.
The end price of £1.2bn, or €1.85bn, is a little higher than expected and is 9.5 times the division's predicted earnings before interest, tax, depreciation and amortisation (EBITDA).
Cadbury, which plans to accept the consortium's binding offer and get the deal through by early 2006, will use the proceeds to pay off some of its £4.3bn in net debt.
If, after consultation with employee representatives, Cadbury does not accept the offer then it will have to pay the consortium five per cent of the offer price. It will also be lumbered with the drinks division for another year.
"Following completion of the deal, we will be able to focus on our faster growing confectionery and other beverage businesses," said Stitzer. The group will hang on to its high cash-generating US drinks arm, including Dr Pepper, Sunkist and 7 Up brands.
Analysts have long touted private equity as a likely suitor for Cadbury's European soft drinks business, with Coca-Cola ruled out due to the resultant market competition fears and PepsiCo only showing limited interest.
The problem for Lion Capital and Blackstone will be what to do with the division going forward.
Like-for-like sales fell one per cent in the first half of 2005, while the firm lost market share across its key markets of France, Spain and Germany in 2004.
Julian Lakin, analyst at Pereire Tod, earlier told BeverageDaily.com that Cadbury's European drinks showed few growth prospects and that private equity firms would be asking: "'In five years, who is going to buy it off us?' That's a problem.
"Private equity firms don't hold things forever, they always need an exit plan," he said, adding it was possible the division would be broken up.
Yet the business is still generating a fair amount of cash and chief executive Stitzer pointed out that "Europe beverages has a great portfolio of brands".
The division, with its sales volume of around 1.7bn litres, is also the third biggest player on Europe's carbonated drinks market; though the top two, PepsiCo and Coca-Cola, are barely visible on the horizon with more than three quarters of the market locked up between them (Coke has around 50 per cent, Pepsi around 18 per cent).