Lezmond Mitchell, a 38-year-old Navajo and convicted murderer, was pronounced dead at 6:29 p.m. EDT (2229 GMT) in the Department of Justice's execution chamber in Terre Haute, Indiana, the department said.
His death was declared 26 minutes after department executioners began injecting him with pentobarbital, a powerful barbiturate, according to a media witness.
He was the fourth man to be executed by the US government this summer after an informal 17-year-hiatus was ended under President Donald Trump, which had been caused in part by legal challenges to lethal injection protocols and difficulties obtaining deadly drugs.
Prior to July, there had only been three federal executions since 1963, all between 2001 and 2003.
Mitchell's lawyers and Jonathan Nez, the Navajo Nation president, had asked Trump, a longtime advocate of capital punishment for serious crimes, for clemency.
On Tuesday night, the US Supreme Court rejected Mitchell's bid for a stay based on his lawyers' argument that racial bias may have tainted the jury at his trial.
Mitchell and an accomplice, Johnny Oslinger, were convicted of murdering a 9-year-old Navajo girl, Tiffany Lee, and her grandmother Alyce Slim in 2001 on the tribe's territory, which spans four states in the U.S. Southwest.
According to prosecutors, the men had been hitchhiking before they stabbed Slim more than 30 times after she gave them a ride. They put the body in the back seat of her truck
alongside the granddaughter as they drove elsewhere before slitting the girl's throat and decapitating both bodies.
Strapped to a gurney before his execution, Mitchell was nonchalant when asked if he had any last words for the victims' relatives watching behind a glass window.
"No, I'm good," he said, according to a media representative allowed to witness the execution. It took about 10 minutes for him to stop moving after the lethal injections began.
Afterward, the eyes of Tiffany's father, Daniel Lee, welled with tears as his lawyer read a statement to reporters.
"I have waited 19 years to get justice for my daughter, Tiffany," the statement said. "But I hope this will bring some closure." The statement added that without the Trump administration's resumption of executions, "I do not think I would have ever received justice or a sense of finality."
Mitchell was sentenced to death in an Arizona federal court over the objection of Navajo officials, who said the tribe's cultural values prohibited taking human life "for vengeance."
At least 13 other tribes joined the Navajo Nation in urging Trump this month to commute Mitchell's sentence to life in prison.
Oslinger was a teenager at the time and ineligible for the death sentence.
Under the Major Crimes Act, the federal government has jurisdiction over certain major crimes occurring on Indian territory, including murder, but usually cannot pursue capital punishment for a Native American for a crime on tribal land without the tribe's consent.