Otto Warmbier, 22, returned to the US last Tuesday, but it emerged he had been in a coma for a year.
North Korea said botulism led to the coma, but a team of US doctors who assessed him dispute this account.
Mr Warmbier was sentenced to 15 years of hard labour for attempting to steal a propaganda sign from a hotel.
He had suffered severe brain damage, and was medically evacuated from North Korea on 13 June to a hospital in his home city of Cincinnati. Ohio. It is unclear how he fell ill.
How harsh is prison in North Korea?
How did Otto Warmbier end up in a coma?
The Warmbier family has blamed his death on torture they say he suffered in North Korea.
"It is our sad duty to report that our son, Otto Warmbier, has completed his journey home. Surrounded by his loving family, Otto died today at 2:20pm," a statement from the family said.
It said the student had been "unable to speak, unable to see and unable to react to verbal commands".
"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."
President Donald Trump said Mr Warmbier's death had deepened his administration's resolve "to prevent such tragedies from befalling innocent people at the hands of regimes that do not respect the rule of law or basic human decency".
"The United States once again condemns the brutality of the North Korean regime as we mourn its latest victim," the presidential statement added.
Mr Warmbier was on holiday with a China-based tour group, which has announced it will no longer take visitors from the US to North Korea.
"The way his detention was handled was appalling and a tragedy like this must never be repeated," Young Pioneer Tours said in a statement.
"Despite constant requests, we were denied any opportunity to meet him or anyone in contact with him in Pyongyang, only receiving assurances that he was fine."
What was medically wrong with Otto Warmbier?
His parents only discovered his medical situation in the days leading up to his release.
Shortly before he was freed, they told the Washington Post news paper they had been informed by the North Korean authorities that their son had contracted botulism, a rare illness that causes paralysis, soon after his trial in March 2016.
He was given a sleeping pill and had been in a coma ever since, the newspaper said.
Media captionOtto Warmbier's father, wearing his son's jacket, told reporters last week his son had been treated "brutally"
But a team of doctors assessing him in Cincinnati said they had found "no sign of botulism" in the student.
"His neurological condition can be best described as a state of unresponsive wakefulness," said Dr Daniel Kanter.
Doctors confirmed that there was no sign he had been physically abused during his detention, based on scans.
They believe respiratory arrest led to his condition, which is caused by a lack of oxygen and blood in the brain.
Who was he?
The economics student from the University of Virginia was travelling in North Korea as a tourist when he was arrested on 2 January 2016.
He appeared emotional at a news conference a month later, in which he tearfully confessed to trying to take the sign as a "trophy" for a US church, adding: "The aim of my task was to harm the motivation and work ethic of the Korean people."
Foreign detainees in North Korea have previously recanted confessions, saying they were made under pressure.
North Korea said it had released Mr Warmbier "on humanitarian grounds".
