"Lithuania has achieved a high degree of sustainable convergence with the euro area, and ... therefore fulfils the conditions for adopting the euro as its currency," the ministers said in a statement.
The move, which must still be approved by EU leaders and reviewed by the European Parliament, paves the way for Lithuania to become the eurozone's 19th member on January 1.
"This really is not the end of the way but just the beginning," Lithuanian Finance Minister Rimantas Sadzius said shortly before the endorsement. "Lithuania will try to be a responsible member of the eurozone," he added.
Earlier this month, the European Commission said the country had fulfilled all conditions. The Eurogroup of 18 eurozone finance ministers added its nod of approval on Thursday.
"This is a well-deserved achievement for Lithuania, after an impressive convergence procedure and remarkable re-emergence from the financial crisis," Eurogroup chief Jeroen Dijsselbloem said of Vilnius' success in meeting the criteria.
Lithuania will be the last Baltic nation to adopt the euro, after Estonia did so in 2011 and Latvia followed suit this year.
EU Economy Commissioner Olli Rehn said the move was a sign of the eurozone's vitality, after the crisis-battered currency bloc pulled out of recession last year.
"Contrary to what the Cassandras were saying some years ago, the eurozone did not break up, but instead it has been enlarged from 16 to 19," Rehn said Thursday.
One outstanding issue is the exchange rate at which Lithuanian litas will be converted into euros. This is to be decided early in July, an EU official said on condition of anonymity.
Lithuania first sought to adopt the euro in 2006. At the time, it failed to achieve the required price stability although it met other criteria, the commission said.
All EU countries except for Britain and Denmark are mandated to join the eurozone once they fulfil its economic criteria. Those still in line are Bulgaria, the Czech Republic, Croatia, Hungary, Poland, Romania and Sweden.
The ministers were also due Friday to consider the commission's 2015 budget proposal, which foresees an annual increase of about 5%, to EUR 142.1 billion (USD 193 million).
The EU's executive has said that the "lion's share" of spending will go into efforts to boost growth and jobs.
EU governments have repeatedly sparred with the parliament over the bloc's budgets. Member states typically seek to limit expenditures, while the legislature has advocated growth-boosting spending.
