The decision, described by NATO head Jens Stoltenberg as "historic," comes 16 years after the alliance bombed Montenegro during the Kosovo war, when it was still part of Yugoslavia, the BBC reports.
Accession talks are expected to take about a year to complete. Montenegro will become NATO's 29th member.
The invitation to Montenegro is NATO's first expansion into eastern Europe since Albania and Croatia joined in 2009.
Besides Montenegro and Georgia, the other current candidates for NATO membership are Bosnia and Herzegovina and Macedonia.
At the same time, Russia has repeatedly warned against the move, describing it as a threat to stability in the western Balkans.
But NATO diplomats say it sends a message to Russia that it cannot veto the alliance's expansion.
However, a Russian foreign ministry spokeswoman said last week that Montenegro's accession would send a "powerful confrontational message."
