The government submitted its request Tuesday, EUobserver reported. If it is granted, the euro would replace the lats Jan. 1.
Recent polls show the move is not popular with the Latvian public. About two-thirds say Latvia should stick with the lats.
The Latvian economy grew steadily in the early years of the new century but crashed with the global economic crisis. It has since made a comeback.
"Latvia's decision to request entry to euro area shows how much progress the country has made to get its economy back on track after the 2008-9 crisis," EU Economics Commissioner Olli Rehn said after he received the application.
Eurozone finance ministers are expected to decide in July if Latvia's petition should be approved. The European Commission and European Central Bank are scheduled to report in June on whether Latvia is ready to join the euro.
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