The UN General Assembly approved a resolution to admit Montenegro as a member in a plenary session of the 191-nation body.
Secretary General Kofi Annan congratulated Montenegro for taking a peaceful and democratic path to independence.
"In achieving its independence through a non-violent and democratic process, conducted in a fair and open way, Montenegro showed the entire world not only its patience but its political maturity," Mr Annan said.
He said the Montenegrin people "demonstrated that adherence to democratic values and the rule of law offer the most effective way to achieve political goals. And they showed that even the most difficult and sensitive problems can be resolved peacefully.
"These are especially important messages given the violent past in the Balkan region."
Neighbourly approach ‘encouraging’
Mr Annan said it was also "encouraging" that Montenegro's neighbours have embraced its independence.
"Montenegro may be small in size and population, but it has a significant role to play in maintaining stability in the region and in promoting good neighbourly relations and cooperation in the Western Balkans,” he said..
In turn, Montenegrin President Filip Vujanovic praised the United Nations, which he said has always represented "an irreplaceable bond among different states, peoples and cultures, particularly at times of crises."
He said he would work to maintain good relations with Serbia and uphold UN tenets, promising in particular to respect international law, defend human rights and help in the fight against terrorism.
"Montenegro has been very proud of its multi-ethnic and multi-religious harmony, as one of its fundamental values, recognisable both in a regional and broader international context,"
Mr Vujanovic said.
After the meeting, Montenegro's flag, a two-headed golden eagle on a red and gold background, was raised in front of the United Nations headquarters in New York.
Home to some 650,000 people, Montenegro declared independence on June 3 after it voted in a referendum to end its 88-year partnership with Serbia.
Serbia only officially recognized it 12 days later.
Montenegro's independence has also been recognized by the European Union, the United States, Russia, China and several other countries.
Montenegro is the last of former Yugoslavia's constituent republics to leave the orbit of Serbia, after Slovenia, Croatia, Macedonia and Bosnia split during the bloody Balkan wars of the 1990s.