An earlier $48bn rescue package for the country's second largest mortgage lender had faltered when a consortium of banks providing a liquidity line declined to participate.
But late on Sunday, Germany's federal financial regulator BaFin said a solution had been found.
Jochen Sanio, chief of BaFin, said: "We have a solution - a good solution."
The announcement came hours after Merkel made another U-turn and pledged that the country would offer an unlimited guarantee for all private savings accounts.
The German leader told all savings account holders "that your deposits are safe. The federal government assures it".
At a mini-summit between the leaders of Europe's four leading nations on Saturday, Merkel had opposed such measures.
Al Jazeera's Nadim Baba explained that Merkel had shifted position, almost admitting that she was under pressure to do exactly what she was criticising other governments, mainly Ireland, for doing, which is guaranteeing the deposits of the entire nation.
The guarantee could, in theory, represent an amount more than $750bn, our correspondent said.
Ireland has announced it is in recession and has already guaranteed bank deposits, as has Greece. With Germany following suit, other European countries were likely to do the same.
Udo Steffens, from the Frankfurt School of Finance, told Al Jazeera that "guaranteeing the savings of mainstream citizens is a positive sign that there will be no bank run or questioning that their private money in the bank is unsafe".
The German government's moves came as BNP Paribas announced on Sunday that it was taking control of the operations of ailing finance group Fortis in Belgium and Luxembourg, in a deal which will make Belgium the largest shareholder in the French bank.
The deal, thrashed out over a weekend of intense talks, leaves the Belgian and Luxembourg governments with reduced holdings in Fortis, which they partly nationalised a week earlier, in exchange for part of BNP Paribas, which becomes the biggest bank in Europe in terms of deposits.
Under the deal, announced by Belgian and BNP officials in Brussels and official sources in Luxembourg, France's biggest bank will take up to 75 per cent of the company's Belgian operation leaving the other 25 per cent, a blocking minority on strategic decisions, in the hands of the Belgian government.
On the Luxembourg side, BNP Paribas will take 66 per cent of the shares leaving the Grand Duchy with 33 per cent, the source said.
On Friday the Dutch government totally nationalised the group's Dutch arm.
The announcements came on the eve of a meeting of European finance ministers in Luxembourg, who will seek to flesh out broad plans for restoring confidence in the crisis-struck banking system, agreed over the weekend by Europe's biggest economic powers.