Federal and state regulators had issued the pipeline the necessary permits to proceed, but the Corps of Engineers had not yet granted it a final easement to drill under a stretch of the Missouri River called Lake Oahe.

The Standing Rock Sioux had objected to the pipeline’s path so close to the source of their drinking water, and said any spill could poison water supplies for them and other reservations and cities downstream. They also said the pipeline’s route through what are now privately owned ranches bordering the river crossed through sacred ancestral lands.

News of the government’s denial came after the size of the camp had swelled with hundreds, perhaps thousands, of Native and non-Native veterans who had arrived to support the tribe. As word spread, people who had camped out here for months, sometimes in bitterly cold temperatures, and who had clashed violently with local law enforcement, linked arms and cheered and cried.

They screamed, “Mni wiconi!” — the movement’s rallying cry — which means “Water is life.”

Jon Eagle Sr., a member of the Standing Rock Tribe, said the announcement was a vindication for the thousands who had traveled here, and for the multitudes who had rallied to the tribe’s fight on social media or donated. Millions of dollars in donations and goods have flowed into the camps for months as the tribe’s fight and the scenes of protesters being tear-gassed and sprayed with freezing water stirred outrage on social media. (Law enforcement officials have insisted the entire time that they have acted responsibly and with restraint.)

“I don’t know quite how to put into words how proud I am of our people,” Mr. Eagle said. “And I mean our people. I don’t just mean the indigenous people of this continent. I mean all the people who came to stand with us. And it’s a beautiful day. It’s a powerful day.”

Ken Many Wounds, who has served as a tribal liaison to express concerns and questions to law enforcement, said he had been standing by the camp’s main fire — one that is tended constantly — when he heard the news from the tribal chairman’s wife. He said he did not believe it at first.

“I hugged her, I cried,” he said. “Our prayers have been answered. A lot of people didn’t believe that prayer was going to be the answer. But our people stayed together. In our hearts, we knew.”