(...) He added he was "convinced" the new deal was better for the Cypriot people than the broader measure rejected by the Cypriot parliament last week, as it focused on two problem banks rather than the entire sector.
IMF head Christine Lagarde said the deal was "a comprehensive and credible plan" to help restore trust in the banking system.
Cypriot Finance Minister Michalis Sarris said he believed the possibility of bankruptcy had been averted.
"It's not that we won a battle, but we really have avoided a disastrous exit from the eurozone," he said.
The deal is being seen as good news by many of Cyprus's small account-holders who have been protected. But officials acknowledge that Cyprus will enter a deep recession and that it will take years to recover, BBC Europe correspondent Chris Morris says.
Many businesses will suffer or shut down, he says.
Under the deal all deposits under 100,000 euros will be secured.
The percentage to be levied on large deposits in the Bank of Cyprus will be resolved in the coming weeks, Mr Dijsselbloem said.
One key element of the deposit tax, demanded by the IMF, is that it should not require approval by the Cyprus parliament.
EU Commissioner for Economic Affairs Olli Rehn said that the "depth of the financial crisis in Cyprus means that the near future will be difficult for the country and its people".