Russia quickly said it would be forced to react to NATO's expansion eastward, with the invitation to the small Balkan country adding to bad blood between Moscow and the West over a host of issues including Ukraine.
NATO chief Jens Stoltenberg, announcing the move at a meeting of the alliance's foreign ministers in Brussels, insisted the "historic" invitation to Montenegro was no one else's business and "not directed at anyone".
Stoltenberg said he expected Montenegro's accession talks to be completed early next year but ratification by the 28 NATO member state parliaments could take some time.
US Secretary of State John Kerry meanwhile played down any threat to Russia from NATO, which has responded to the Ukraine conflict with a military upgrade to reassure nervous ex-Soviet states they need not fear a more assertive Russia.
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Montenegro's Foreign Minister Igor Luksic said the decision reflected the great efforts his country had made to modernise and meet western civil society norms.
"It is a great day for my country and for the alliance ... It is great news for the western Balkans, for its unity and security," Luksic said.
Russian President Vladimir Putin has bitterly complained of what he sees as a hostile NATO encroachment on his country's borders and Moscow was blunt in response today.
Montenegro, a Balkans country of just over 600,000 people, won its independence in 2006 following the bloody break-up of what was Yugoslavia and the end of a federation with Moscow's long-time ally Serbia.
Its army has 2,000 soldiers, and it has contributed 25 soldiers to the NATO-led mission in Afghanistan since 2010.
Russia has traditionally been a close ally of Montenegro and several thousand Russians live there, but relations have soured since Montenegro joined EU-led sanctions against Russia over Ukraine.