After being famously for their neutrality, Sweden is set to join the NATO military alliance.

The North Atlantic Treaty Organization on Wednesday formally invited Finland and Sweden to join the military alliance — a major blow to Russian President Vladimir Putin, who has fiercely opposed NATO expansion.

“The accession of Finland and Sweden will make them safer, NATO stronger and the Euro-Atlantic area more secure. The security of Finland and Sweden is of direct importance to the Alliance, including during the accession process,” the alliance said in a statement.

Now the decision will go to the 30-member alliance’s individual parliaments and legislatures for final approval. In the statement, NATO leaders said they expect the process will move quickly.

The historic expansion of NATO comes after Turkish President Tayyip Erdogan reversed his objections to expanding the alliance.

President Biden said the move is a major rebuke to Russian President Vladimir Putin, who raged over NATO’s expansion and used it as a pretext for his war in Ukraine.

Mr. Putin was betting that NATO would be fractured over the war in Ukraine and he could exploit the weakened alliance to expand Russian territory. That plan, Mr. Biden said, has backfired.

“I said Putin’s looking for the Finlandization of Europe. He’s going to get the NATOization of Europe,” Mr. Biden said, referencing Finland’s status as a neutral country. “And that is exactly what he didn’t want, but exactly what needs to be done to guarantee security for Europe. And I think it’s necessary.”

Mr. Biden is also committing additional U.S. forces in Europe to bolster NATO and fend off threats “from all directions, across every domain.”

“The United States and our allies, we are going to step up — we are stepping up. We’re proving that NATO is more needed now than it ever has been and is as important as it ever has been,” the president said.

He pledged to increase the number of troops stationed in Europe by establishing a permanent headquarters for the 5th Army Corps in Poland, maintaining an extra rotational brigade of 3,000 troops in Romania, increasing rotational deployment to Baltic states and sending two more F-35 fighter jet squadrons to the United Kingdom.

Mr. Biden also said the U.S. would add air defense and other capabilities in Germany and Italy. On Tuesday, he announced plans to send two additional Navy vessels to Spain.

“We’re sending an unmistakable message, in my view, that NATO is strong and united and the steps we are taking during this summit are going to further augment our collective strength,” Mr. Biden said.

NATO Secretary-General Jens Stoltenberg hailed the new U.S. military force posture, saying it underscores Mr. Biden’s leadership and commitment to the alliance.