(Updates with shareholders approval, executive comment)
ATHENS, April 30 (Reuters) - Greece's fourth-biggest lender Eurobank won approval on Tuesday from its main shareholder National Bank for a capital injection that makes it the first major Greek bank to fall under state control as a result of the debt crisis.
Greece's four major banks including Eurobank need 27.5 billion euros in fresh funds to restore their solvency ratios to levels required by the country's central bank after incurring losses from a sovereign debt writedowns and impaired loans.
Another of the four, National Bank, agreed to its own 84.3 percent holding in Eurobank being diluted to the low single digits by an issue of shares to the government's Hellenic Financial Stability Fund (HFSF) in return for 5.84 billion euros in capital.
The shares will be issued at 1.541 euros each after a 10-for-1 reverse split, Eurobank's Chief Financial Officer Paula Hatzisotiriou told shareholders.
Private shareholders still have stakes in each of the four banks but their value is set to dwindle as injections of capital formalise the official life support on which they rely to continue operating.
Eurobank executives said the bank hoped to return to private hands at a later stage and the country's bailout program requires the bank fund to sell off its stake after three years.
"Our return to the private sector is the bank's main goal, to return where we belong as soon as possible," Eurobank's Chairman Efthymios Christodoulou told shareholders.
Eurobank dropped efforts to plug part of its capital hole by tapping shareholders and private investors after plans to integrate with parent NBG into a single banking group were suspended following objections from Greece's international lenders.
Executives said uncertainty on whether the plan to merge with parent NBG would proceed had hurt its investment case during efforts to get commitments by private investors to take part in the capital boost via a rights offering.
Eurobank and NBG are still waiting for the bank rescue fund to make a final decision on whether their integration should proceed.
"If authorities decide against the merger, Eurobank will submit a business plan to attract private strategic and institutional investors from Greece and abroad," CEO Nick Nanopoulos said, adding the bank could become a "fourth pillar" for further restructuring in the banking sector.
Rivals Piraeus and Alpha Bank are expected to meet a 10-percent required private sector participation in their recapitalisation to retain management control.
NBG has also said the 10 percent target is attainable and that it is aiming to get private investors to subscribe to 12 percent of its share offering. (Reporting by George Georgiopoulos, editing by Deepa Babington and Patrick Graham)