The two banks, which were ordered by the central bank to be liquidated in September 2013, will return their banking licences next week.
They will then be folded into the Bank Assets Management Company (BAMC), the bad bank, and cease operating as independent entities, Dragonja said.
The initial plans, cleared by the EU, predicted Probanka and Factor banka would be fully wound down by the end of the year.
The banks have offloaded the vast majority of their assets and liabilities ahead of schedule and paid all depositors.
The assets they have left are not liquid and they would have to sell it under time pressure, Dragonja said.
The folding into the bad bank will not have any negative fiscal consequences. Both banks have positive capital and will be able to settle their outstanding liabilities to the state, he said.
Dragonja was speaking at a session of the opposition-controller Commission for the Oversight of Public Finances.
Opposition MPs wanted to know why the government opted for a simplified merger through acquisition.
Dragonja said this was the best way to ensure they are wound down without there being a negative impact on public finances or the bad bank.