The Abu Dhabi Investment Authority will invest $7.5 billion in Citigroup, offering the nation’s largest bank needed capital to offset big losses from mortgages and other investments.

The cash from the sovereign investment fund of the Gulf Arab state, which has benefited from this year’s surge in oil prices, will be convertible into no more than 4.9% of Citigroup Inc.’s equity. Citigroup characterized the investment as passive and said the fund will not be able to name any board members to the bank.

The Investment Authority will receive equity units that pay an 11% annual yield — a high price for Citigroup, whose dividend yield is 7.3%. They will then be converted into Citigroup common shares at a price of up to $37.24 a share between March 15, 2010, and September 15, 2011.

The purchase, announced late yesterday, would make the Investment Authority one of Citi’s largest shareholders.

“We see in Citi a highly respected company with a premier brand and with tremendous opportunities for growth,” the Investment Authority’s managing director, Sheikh Ahmed Bin Zayed Al Nahayan, said. “This investment reflects our confidence in Citi’s potential to build shareholder value.”

The investment, which was expected to close within the next several days, will be considered Tier 1 capital for regulatory purposes. That will help Citi reach its goal of returning to its target capital ratios — essentially, its ratio of cash to debt — in the first half of 2008, the bank said.

Tier 1 capital describes a company’s core cash, which includes stock and disclosed reserves. When a company has a high amount of Tier 1 capital in relation to its debt, the company is regarded as financially strong.

A Banc of America Securities analyst, John McDonald, said the investment will buy Citi some time, but will not fix the bank’s debt troubles. “Capital infusions do not solve problems overnight,” he wrote in a research note.

Investors, however, were relieved by the infusion and Citigroup shares rose 98 cents, or 3.3% to $30.78 at the open of trading today.

Citigroup’s shares have lost about 45% of their value since the beginning of this year, wiping away $124 billion in market capitalization, and touched a five-year low yesterday as the drumbeat of bad news about its investment losses has grown more persistent.

Charles Prince stepped down as Citigroup’s chairman and chief executive November 4, the same day Citi announced that it will likely write down the value of its portfolio by $8 billion to $11 billion in the fourth quarter.

In the third quarter, the bank’s exposure to assets tied to subprime mortgages led to a loss of about $6.5 billion.

Citigroup executives said yesterday that a deteriorating business climate could mean a new round of job cuts, even after the bank pared its 320,000 workforce by 17,000 positions earlier this year. Pummeled by billions in writedowns, Citigroup is reviewing its cost structure to bring it in line with “economic realities,” the company said.

Analysts believe the Investment Authority is the world’s largest sovereign wealth fund, although the fund has never publicly revealed its total assets. Analysts estimate the fund controls hundreds of billions of dollars, with some experts saying the amount could be approaching nearly a trillion dollars.

Sovereign funds throughout the Middle East have been building up overseas investments recently, much of it on the back of oil prices that have risen more than 60% this year, bringing record cash flow to the region. China and Russia also have considerable funds they are sending overseas.

Unlike its counterparts in Dubai, the Investment Authority provides very little information about its investments, with analysts saying it appears to regularly purchases less than 5% of the companies it targets to avoid having to disclose the investments.