Otto Warmbier, 22, who was arrested in North Korea while visiting as a tourist, had been described by doctors caring for him last week as having extensive brain damage that left him in a state of "unresponsive wakefulness."
"Unfortunately, the awful torturous mistreatment our son received at the hands of the North Koreans ensured that no other outcome was possible beyond the sad one we experienced today," the family said in a statement after Warmbier's death at 2:20 p.m. EDT (1820 GMT).
His family has said that Warmbier lapsed into a coma in March 2016, shortly after he was sentenced to 15 years of hard labor in North Korea.
Physicians at the University of Cincinnati Medical Center, where he died, said last Thursday that Warmbier showed no sign of understanding language or awareness of his surroundings, and had made no "purposeful movements or behaviors," though he was breathing on his own.
There was no immediate word from Warmbier's family on the cause of his death.
The circumstances of his detention in North Korea and what medical treatment he may have received there remained a mystery, but relatives have said his condition suggested that he had been physically abused by his captors.
The University of Virginia student and Ohio native was arrested, according to North Korean media, for trying to steal an item bearing a propaganda slogan.
North Korea released Warmbier last week and said he was being freed "on humanitarian grounds."
The North Korean mission to the United Nations was not available for comment on Monday.
U.S. President Donald Trump issued a statement offering condolences to the Warmbier family and denouncing "the brutality of the North Korean regime as we mourn its latest victim."