Campbell came in third place on the ITV talent show Pop Idol in 2002, behind Will Young and Gareth Gates.
The cause of death has not been specified but the Scot was found in his apartment in Minnesota, according to his family.
“It is with great sadness that we announce the passing of Darius Campbell Danesh,” they said in a statement.
“Darius was found unresponsive in bed in his apartment room in Rochester, Minnesota, on August 11 and was pronounced dead in the afternoon by the local medical examiners’ office.
“The local police department have confirmed that there were no signs of intent or suspicious circumstances. The cause of his sudden death is unknown at this stage while medical examinations continue.
“We ask that you kindly respect our wishes for privacy at this time whilst we come to terms with the tragic loss of our son and brother.”
Following his relative success on the ITV talent shows, Danesh scored a number one in the UK with the track ‘Colourblind’ before achieving a Top 10 album with Dive.
The singer then turned his hand to musicals on the West End, appearing in the likes of Chicago and the Olivier award-winning Guys and Dolls.
He also featured as Rhett Butler in Sir Trevor Nunn’s 2008 musical adaptation of Gone with the Wind and had cameo appearances in Hollyoaks and Hotel Babylon, and also participated in the first series of ITV’s Popstar to Operastar in 2010.