The Utah Department of Corrections said the 38-year-old had been suffering from "chronic, degenerative conditions".
A spokesman said Rossi died in a local hospital on Thursday after "he chose to remove himself from the care that was being provided".
Rossi was found guilty of raping two women in Utah in 2008 after two separate trials in 2024.
He was ordered to serve two sentences of between five years and life consecutively.
Rossi had fled to Scotland in 2021 in an attempt to evade justice but was arrested in the Covid ward of a Glasgow hospital.
Staff had recognised his mugshot and distinctive tattoos from an Interpol wanted notice - but he claimed to be an Irish-born orphan called Arthur Knight, who had never been to America.
He gave an interview to the BBC, where he maintained his story - but could not produce a birth certificate or a passport.
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The story of Nicholas Rossi, the US fugitive who faked his own death
Rossi continued to insist at a series of hearings at Edinburgh Sheriff Court - which he usually attended in an electric wheelchair, wearing an oxygen mask, hat and three-piece suit - that he was the victim of mistaken identity.
He was finally extradited to the US in January 2024, more than a year after the court had ruled that he was indeed Nicholas Rossi.
He was convicted in separate trials in August and September that year of raping two women in Utah in 2008.
Image source, Utah Department of CorrectionsImage caption, Rossi was jailed in Utah in 2024 after being found guilty of rape
Born Nicholas Alahverdian in Rhode Island in 1987, Rossi spent time in care as a teenager and went on to become a child welfare campaigner.
Reports of his death emerged in 2020, but the authorities suspected Rossi had fled to the UK after discovering that the FBI were investigating an alleged credit card fraud.
The Big Cases: Unmasking a Fugitive
The story of Nicholas Rossi, the US fugitive who came to the UK with a new identity after faking his own death.
Watch on iPlayerHis online footprint ultimately led police to the hospital in Glasgow, where he was identified by staff.
Rossi insisted that he had been given his distinctive tattoos while he was lying unconscious in the hospital in an attempt to frame him.
Image source, PA MediaImage caption, Rossi regularly attended court hearings in Edinburgh wearing an oxygen mask
He sacked several lawyers before a sheriff eventually ruled in 2023 that he was Nicholas Rossi, and that his mistaken identity claim was "implausible" and fanciful".
He was flown back to America in January 2024 after failing to overturn the decision. Several months later, he admitted his real identity during a bail hearing in Salt Lake City.
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US fugitive Nicholas Rossi jailed for raping two women
US fugitive Nicholas Rossi who fled to Scotland sentenced for rape
Fugitive Nicholas Rossi found guilty of second rape in US
