The EU foreign ministers said the June 3 independence declaration by Montenegro's parliament was legal confirmation of the outcome of a referendum two weeks earlier, in which 55.5 percent of Montenegrins voted to end their union with Serbia.
That split dissolved the last vestiges of the former Yugoslavia.
The EU ministers said they will craft close ties with Montenegro "as a sovereign, independent state" and urged the Podgorica government "to pursue a direct and constructive dialogue" on its future relations with Belgrade.
Both Serbia and Montenegro are to join the EU, though neither has been formally declared a candidate for membership.
The EU foreign ministers reaffirmed "the European perspective of the Western Balkans" — whose wars of the 1990s have kept the region out of the EU while other east European nations joined.
The population of Montenegro is 620,000, predominantly Christian Orthodox Slavs. Up to 15 percent are Slavic Muslims. Ethnic Albanians account for 7 percent.
The country was recognized as an independent state in 1878 when it became a monarchy. After World War I in 1918, it merged with Serbia and some Slav-populated parts of the former Austro-Hungarian Empire to form what later became Yugoslavia. After World War II, communists took over the country, which unraveled along ethnic lines in the 1990s.