By William Horsley
BBC European affairs correspondent
The Latvian Yes vote means that all nine of the new member states which held referendums won the consent of their populations for joining the European Union.
The tenth newcomer, Cyprus, decided for the EU through a parliamentary vote.
Czechs are the latest nation to vote for EU membership
It is a big relief for each of the governments concerned. And a big relief for the leaders of the EU's own institutions.
All the newcomers to the EU will formally take their place in the Union next May, thanks to the positive votes in referendums in Malta, Slovenia, Hungary, Lithuania, Slovakia, Poland, the Czech Republic, Estonia and Latvia.
The most enthusiastic for the EU were Lithuania and Slovakia, with more than 90% in favour.
The least decided was Malta, with its 54% Yes vote.
The votes were held during a turbulent time for the EU, with bitter feuds among various members and prospective members over Iraq, relations with the United States, the EU's internal economic management and its future constitution.
EU constitution debate
What happens now?
Quite soon the newcomers will be confronted, like the existing EU member states, with the need to gain approval at home for the EU constitution.
Already it has proved very contentious, and the text must be finalised before the official moment of enlargement, which will expand the EU to 25 countries.
Then it will be referendum time again - on the constitution - in many countries of both western and eastern Europe.
The EU is a work in progress. But now for the first time the new members, mostly nations which endured decades of Soviet-style communism, will have a full say in its future.