Under the plan, the banks' soured loans, as well as legal risks stemming from a mis-selling scandal, will be moved to a bad bank, partly financed by the state.
Veneto Banca and Banca Popolare di Vicenza have always been experiencing difficulties, while the government has tried to recapitalize the two lenders.
The move comes less than a month after the European Union anti-trust authority approved Italy's massive rescue of the country's troubled third-largest bank, Monte dei Paschi di Siena (BMPS), which has been in deep trouble since the worst of the eurozone debt crisis.
The banks, both located in the Veneto region in Italy, were being monitored by the ECB since 2014, after one of its evaluations had shown capital shortfalls.More news: Doctors: Officer stabbed in neck at airport recovering well
Intesa Sanpaolo, Italy's largest bank, will take control of the banks' so-called "good assets" after paying the symbolic price of €1.
"The announcement of definitive steps to resolve the two Veneto banks should be seen as a positive for Italian banks and the broader sector (albeit at a high cost)", said Jefferies analyst Benjie Creelan-Sandford.
The Finance Ministry has said all measures would be taken to ensure that senior creditors and depositors are protected in their liquidation under the national insolvency law, and customers would see no interruption in service.
Markets reacted positively, as investors seemed to welcome the move to clean up Italy's banking problems.More news: Trump under investigation over alleged obstruction of justice
By avoiding the SRB, Italian authorities could work under a softer set of rules dating from 2013 and only had to put forward a state-aid case to the commission.
"I am very disappointed that the commission has approved this course of action".
However, Bank of Italy officials said the final bill for the state would be small and some money could be recovered from the management and sale of the two banks' bad loans. The two banks have a combined capital shortfall of about EUR6.4 billion. That's because a government decree of several months ago already provided for the resources for bank rescues. The government has a claim on whatever can be recovered from the loans and other investments that are being wound down.
-Julia-Ambra Verlaine contributed to this article.More news: DUP and Conservatives make confidence and supply deal worth £1.5bn
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