* Unipol Gruppo offers 2.7 euros per share to buy out UnipolSai

* Or UnipolSai investors can choose 3 for 10 share offer

* Unipol Gruppo shares jump 20%, UnipolSai's climb 12%

Feb 16 (Reuters) - Italian financial group Unipol Gruppo announced on Friday an offer for the 14.75% of UnipolSai it does not already own, valuing the insurer at 7.64 billion euros ($8.23 billion) in a deal aimed at simplifying the group's structure.

Shares in Unipol Gruppo jumped as much as 20.4% after the long-awaited move. Shares in Italy's second-largest insurer UnipolSai, whose board approved the offer, rose as much as 12.4%.

Unipol Gruppo will offer 2.70 euros for each UnipolSai share it does not already own, a premium of 12.6% to UnipolSai's Feb. 15 closing price, the group said.

Alternatively, it will offer three of its own shares for every 10 UnipolSai shares, allowing shareholders in UnipolSai to become investors in Unipol Gruppo.

Unipol Gruppo said it would use its own financial resources for the deal.

The cash offer, if taken in full, would be worth 1.13 billion euros.

The group will change its name to Unipol Assicurazioni SpA after the deal, which is expected to close by the end of 2024.

The deal is intended to simplify the structure of the two businesses and create a single listed company on the Milan Bourse.

UnipolSai also said its 2023 consolidated net profit rose to 766 million euros from 651 million euros in 2022.

It proposed a dividend per share of 0.165 euros, versus 0.16 euros the previous year.

Direct insurance income from non-life business, UnipolSai biggest revenue earner, was up 4.2% year-on-year at 8.7 billion euros, while income from life business jumped 20% to 6.4 billion euros "despite ongoing market difficulties due to a general increase in interest rates," the company said.

UnipolSai's combined ratio - a measure of profitability for its property and casualty division - was 98.2% at the end of December, improving from 98.6% in September. Readings below 100% indicate profitability. ($1 = 0.9293 euros) (Reporting by Alberto Chiumento; Editing by Muralikumar Anantharaman and Mark Potter)