Slovenian authorities offered the concession after the European Commission opened a full-scale investigation in January following a delay in the sale. Slovenia had granted up to 2.32 billion euros (£2.1 billion) in state aid to NLB in recent years.
The EU competition enforcer said the country's latest measure complied with the bloc's rules ensuring a level playing field.
"Slovenia has firmly committed to an ambitious time schedule for NLB's sale with a first sale tranche of at least 50 percent plus one share by the end of 2018," the Commission said in a statement.
It said Slovenia set out strict deadlines to complete the sale of 75 percent minus one share of NLB by the end of 2019. If it misses the deadline, a trustee will take over the sales process.
NLB will also only be allowed to grant new loans if it receives a minimum return on equity on those loans and not-enter businesses it has sold off as part of its restructuring.
(Reporting by Foo Yun Chee; editing by Robert-Jan Bartunek)