Abu Dhabi is the richest of the seven emirates, among them Dubai, that make up the Gulf country of UAE.
The capital injection will shore up Citi's balance sheet, which has been hurt by about $6.8bn of write-offs and losses in the third quarter, and the potential for another $11bn in the fourth quarter.
The Wall Street Journal said on its website that as a result of the deal, ADIA will become one of Citigroup's largest shareholders; its take will exceed that of Saudi Prince Alwaleed bin Talal, long known as one of Citigroup's largest shareholders, according to a person familiar with the situation.
Citi is paying a high price for the capital injection by selling mandatory convertible securities to ADIA, which pay a fixed coupon of 11 per cent.
The sale to the $650bn ADIA, the world's largest sovereign wealth fund, may also signal the free fall in US financial stocks is close to ending, analysts said.
Sheikh Ahmed Bin Zayed Al Nahyan, the ADIA managing director, said: "We see in Citi a highly respected company with a premier brand and with tremendous opportunities for growth.
"This investment reflects our confidence in Citi's potential to build shareholder value."
Win Bischoff, acting chief executive of Citigroup, said in a statement: "This investment, from one of the world's leading and most sophisticated equity investors, provides further capital to allow Citi to pursue attractive opportunities to grow its business.
"This investment also enables us to access capital in an efficient manner, and is consistent with our strategy of maintaining a balance sheet that benefits from highly diverse sources of funding in terms of both geography and type of security."
Citigroup's shares have lost about 45 per cent of their value since the beginning of this year, wiping away $124bn in market capitalisation.
Shares rose on Tuesday by more than two per cent, or $2.10, to $31.86, in pre-market trading, after touching a five-year low Monday.
Sovereign funds throughout the Middle East have been building up overseas investments, much of it on the back of oil prices that have risen more than 60 per cent 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, ADIA provides very little information about its investments, with analysts saying it appears to regularly purchase less than five per cent of the companies it targets to avoid having to disclose the investments.
Stake in Sony
On Monday, Dubai International Capital (DIC), which is owned by the ruler of the emirate of Dubai, announced that it acquired a stake of undisclosed size in the Japanese electronics and media company Sony.
DIC's other investments this year included acquiring a 3.12 per cent of EADS which builds Airbus' commercial and military aircraft.
The firm also holds stakes in Daimler AG and British bank HSBC Holdings PLC.
Many companies have welcomed such investments because the funds tend to be stable investors, but some US officials have expressed concern that their acquisitions could target sensitive industries with links to national security.