BRUSSELS — The small European country now known as the Republic of North Macedonia may not seem like a significant addition to NATO. But it plugs another gap in what was once the former Soviet Union’s backyard, and comes at a time when East-West tensions are rising.

North Macedonia’s inclusion also means NATO will soon have 30 members, all committed to their collective defense. That is double what NATO’s membership was in 1991, when many experts thought the alliance would disband with the collapse of the Soviet Union and the Warsaw Pact.

On Wednesday, in a ceremony at NATO’s Brussels headquarters, member countries formally signed a letter of accession for North Macedonia, which should become a full member by year’s end.

Political analysts said the addition was a setback for President Vladimir V. Putin of Russia, who sees NATO as an expansionist military force on his country’s doorstep. Mr. Putin has for many years argued that NATO is no longer needed because, he says, Russia poses no threat.