The Belgian government will buy the bank’s division in Belgium for 4bn euros ($5.4bn; £3.4bn).
And Luxembourg’s finance minister said a Qatari investment group was ready to buy the bank’s Luxembourg unit.
The plan came after German Chancellor Angela Merkel and French President Nicolas Sarkozy agreed Europe’s crisis-hit banks needed to be recapitalised.
Dexia also secured state guarantees of up to 90bn euros to secure borrowing over the next 10 years. Belgium will provide 60.5% of these guarantees, France 36.5% and Luxembourg 3%, the bank said in a statement.
Belgian Prime Minister Yves Leterme told a news conference in the early hours of Monday: “We found an agreement on the fair division of the costs related to the management of the ‘rest bank’.”
The Belgian unit is a largely retail operation of 6,000 staff, handling deposits totalling 80bn euros for four million customers.
Dexia asked for help for the second time in three years after a liquidity squeeze sent its shares tumbling.
It had to be bailed out in 2008, with the Belgian, French and Luxembourg governments putting in 6.4bn euros to keep it afloat.
The latest announcement came after a board meeting that lasted some 14 hours from mid-afternoon on Sunday.
Dexia’s near-collapse is the latest warning sign over the health of Europe’s lenders. It has a global credit risk exposure of around $700bn, twice the gross domestic product of Greece.
BBC business editor Robert Peston said that given the size of Dexia, with a balance sheet of over 500bn euros, eurozone governments viewed its rescue as vital to avoid more market turmoil.
Under the plan, Dexia’s French municipal finance operations will come under state control. The bank is also expected to announce the planned sale of its healthy businesses, such as Denizbank in Turkey.
The burden of bailing out Dexia led to a warning from the ratings agency Moody’s that it could cut its rating on Belgium’s government bonds.
Earlier on Monday, Belgian bank KBC said it was selling its Luxembourg unit, KBL European Private Bankers, to Qatari investment group Precision Capital for 1.05bn euros.
KBC said the sale would allow it to raise capital, reduce its risk profile and focus on its core markets of Belgium and central and eastern Europe.
Luxembourg Finance Minister Luc Frieden said the same investment group, which belongs to members of the Qatari royal family, was ready to buy Dexia’s Luxembourg unit, BIL.
“The KBC Group has informed [us] that it has sold KBL to an investor from Qatar… The fact that this family group has bought one entity (KBL) and intends to buy the other (BIL) is good for the Luxembourg financial sector,” he told a news conference.
The Luxembourg government itself still aimed to take a minority stake in BIL, though the size of the investment had not yet been agreed, he said.