He was returned to the US last Tuesday, with North Korea saying it was on humanitarian grounds.
North Korea said he had been in a coma for a year after contracting botulism but his family say he was subjected to "awful torturous mistreatment".
A team of US doctors have also disputed North Korea's version of events.
Mr Warmbier 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.
A statement from the family on Monday said: "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."
They 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."
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