MILAN - Italian energy group Eni said on Thursday that U.S. fund KKR would take a 25% stake in Enilive, in a deal that values the entire biofuel business at 11.75 billion euros ($12.7 billion) including debt.

KKR's 2.938 billion euro purchase of the stake improves Eni's financial position while ensuring that it retains control of Enilive, the Italian company said.

The agreement is part of Eni's strategy to spin off growth businesses through co-investors.

The transaction will be through a 500 million euro capital increase for Enilive, which will be reserved for KKR, plus the sale of Enilive shares owned by Eni for 2.438 billion euros.

Eni will also inject 500 million euros into Enilive before the KKR deal closes, ensuring the business is debt-free.

"This agreement marks a significant further step in our business strategy related to the energy transition," Eni Chief Executive Claudio Descalzi said in a statement.

JP Morgan and Mediobanca acted as financial advisers for Eni. Deutsche Bank and Unicredit were financial advisers for KKR, with Kirkland & Ellis and Gianni & Origoni serving as legal counsel.

In a similar deal last March the Italian energy group opened up the capital of its retail and renewables subsidiary Plenitude, handing over a minority stake to Swiss asset manager Energy Infrastructure Partners.

($1 = 0.9270 euros)

(Reporting by Francesca Landini Additional reporting by Claudia Cristoferi Editing by Gianluca Semeraro and David Goodman)