Qatar's Al-Thani family will acquire 90 percent of Banque Internationale Luxembourg (BIL) via their Precision Capital investment group, Dexia said.
The deal follows Precision's agreement in October to buy the private banking business of Dexia's Belgian rival KBC
Morgan Stanley estimated the value of BIL at 1.0-1.7 billion euros in October, with reports at the time saying the overall price was likely to be around 1 billion euros..
"It (the price) looks a bit low," KBC Securities analyst Dirk Peeters said.
"But everyone knows that Dexia have to sell. They may have been willing to pay 800 to 900 million euros, but thought they'd put in a lower offer."
KBC has a 'reduce' rating on Dexia shares, with a 0.10 euro price target.
Dexia was bailed out by Belgium, France and Luxembourg in October, with Belgium nationalising Dexia's Belgian banking business.
Luxembourg will buy the remaining 10 percent of BIL, Dexia said.
Qatar has previously invested in European banks, among them British lender Barclays in an emergency fund-raising three years ago.
Dexia BIL's stakes in Dexia Asset Management Luxembourg and RBC Dexia Investor Services will be sold separately. Its portfolio of legacy securities and stakes in Dexia LDG Banque and Parfipar will be transferred to Dexia.
The BIL sale is a further step towards dismantling Dexia. French state bank Caisse des Depots and La Banque Postale, France's post office bank, are to take stakes in French financing arm, Dexia Municipal Finance.
Dexia also has to dispose of its 50 percent stake in a joint venture with Royal Bank of Canada, RBC Dexia Investor Services, as well as Dexia Asset Management and its fast-growing Turkish operation, DenizBank.
The group has secured temporary financing guarantees from Belgium, France and Luxembourg of 45 billion euros to cover its borrowings for six months, but has still to secure such guarantees for the longer term.
