In a long-sought victory for the gay rights movement, the Supreme Court ruled by a 5-to-4 vote on Friday that the Constitution guarantees a right to same-sex marriage.

“No longer may this liberty be denied,” Justice Anthony M. Kennedy wrote for the majority in the historic decision. “No union is more profound than marriage, for it embodies the highest ideals of love, fidelity, devotion, sacrifice and family. In forming a marital union, two people become something greater than once they were.”

Marriage is a “keystone of our social order,” Justice Kennedy said, adding that the plaintiffs in the case were seeking “equal dignity in the eyes of the law.”

The decision, which was the culmination of decades of litigation and activism, set off jubilation and tearful embraces across the country, the first same-sex marriages in several states, and resistance — or at least stalling — in others. It came against the backdrop of fast-moving changes in public opinion, with polls indicating that most Americans now approve of the unions.

The court’s four more liberal justices joined Justice Kennedy’s majority opinion. Each member of the court’s conservative wing filed a separate dissent, in tones ranging from resigned dismay to bitter scorn.

In dissent, Chief Justice John G. Roberts Jr. said the Constitution had nothing to say on the subject of same-sex marriage.