EU officials say that Latvia's desire to join is a vote of confidence in the shared currency and disproves predictions that the eurozone might break up.
The current 17-country group has struggled since 2009 with too much government debt, compounded now by a slack economy.
The European Commission gave the thumbs up after a required review. A final decision will be made by eurozone finance ministers July 9.
To join, Latvia had to show it could control inflation, deficits and government debt. Still, many Latvians are sceptical and anti-euro parties won more than half the vote in elections in the capital, Riga, last weekend.
Olli Rehn, the EU's top economic and monetary official, said Latvia's membership bid was "further evidence that those who predicted the disintegration of the euro area were wrong".
Latvians suffered through several years of enforced government austerity in order to fulfill the requirements to join the euro. The country also went through a profound recession after a credit-fuelled real estate boom collapsed. The economy shrank by around 25% in 2008-2010 but has now returned to strong growth.
This could undermine the stability of the banks - a problem that was at the centre of the recent rescue of Cyprus, the latest eurozone member to receive a bailout.
In a separate assessment, the European Central Bank said that Latvia would need to exercise continued vigilance to make sure inflation stayed under control and that its banks were strong enough. It called non-resident deposits "an important risk to financial stability".