The Italian plan instead takes advantage of an exception to European Union bank rules that allows the use of routine insolvency proceedings with banks not considered systemically important, allowing the process to be handled by the member state.
Italian banks have been a concern for years, weighed down by about EUR200 billion in bad loans, low profitability and insufficient capital.
The European Commission ended months of speculation over whether Italy would be able to bypass regulations preventing state bailouts of banks by granting approval for the deal.
Because financial markets open on Monday, the process was completed over the weekend.
European shares rose on Monday as banks rallied after Italy reached a deal to wind up two failed regional banks and Nestle climbed to a new record after an activist investor urged changes at the consumer bellwether.
"The use of state aid should be avoided as much as possible in bankruptcy cases", a spokeswoman for finance minister Wolfgang Schaeuble said, adding that it was up to the European Commission to ensure that the rules were respected. It ruled they were "failing or about to fail", and they will now face insolvency proceedings in Italy.More news: Supreme Court to consider whether partisan election maps are unconstitutional
Italian lenders are saddled with roughly €360 billion ($400 billion) in bad loans, roughly a third of the eurozone total.
"Italy will support the sale and integration of some activities and the transfer of employees to Intesa Sanpaolo", and said the action will "also remove $18 billion ($20 billion) in non-performing loans from the Italian banking sector and contribute to its consolidation".
Those plans appear to contradict newly-adopted rules on bank rescues, in the form of the Bank Recovery and Resolution Directive, which demand that depositors and investors are "bailed-in" before taxpayers' funds are used, although national regulators are permitted to circumvent them if they deem their use would result in systemic financial risks as a result. Such investors were an important driver of equity and corporate bond selling in 2015 and early 2016, the strategists said.
In Frankfurt, insurer Allianz rose 0.55 percent after selling its 90 percent stake in regional bank Oldenburgische Landesbank to US private equity firm Apollo.
Sunday's announcement comes less than a month after Spain's Banco Popular was rescued by Santander.
But the rules did require that holders of less secure junior bonds won't be paid back, and thousands of small shareholders will lose their already diminished investment.
"Some in Italy will see this last turn as a happy ending", wrote Silvia Merler, a scholar affiliated with the Bruegel think tank in Brussels, in a blog post.
While German politicians were among the most vocal critics, lawmakers from other countries also expressed dismay.