Councillor Barrett and his wife Moira had served as first citizens since May 2003.
Council leader Bill Taylor said: 'His death is a very sad loss for Michael's family and our thoughts go out to them. I had known Michael for 30 years and knew him to be a man who was a champion for ordinary people.
'Discussions with his family are taking place for the arrangements for the civic funeral and as a mark of respect the local labour party suspended campaigning in the local election for the day.'
Councillor David Foster, deputy mayor said: 'His death is a sad loss to the council. He was well respected across all parties. He has done a really good job as mayor and he carried on with his duties even when he was ill - it was typical of him to put service to the community before his own health.'
Colin Rigby, leader of the Conservative group on the council said: 'Michael was a very good ward councillor and worked very hard for vulnerable people in the community. In his personal life he was absolutely committed to his family and his grand children and he should be commended and remembered for that.'
Councillor Barrett has had three separate stints as a councillor for the borough. He was first elected in 1976 and served until May 1983.
He was later elected in 1995 before being elected for his most recent Earcroft ward in May 1997.
He was re-elected to the ward in 2001 and served his local community until his death.
Phil Watson, chief executive of the council said: 'I am sorry to have to confirm the sad news that the Mayor passed away during the night. We send our condolences to his family at this sad time. As a mark of respect, all mayoral engagements, which would normally have been carried out by the deputy mayo r, have been cancelled until after the funeral.
'We are discussing the arrangements with the mayoress and the cathedral authorities and we expect the service to take place next week.'
The chief executive is also returning officer of the forthcoming local elections he added: 'The local election in the Earcroft ward has been cancelled as a result of the mayor's death and a coventional by-election will be held within 35 days of 10 June. Postal elections for other seats in the borough are unaffected and voters in Earcroft will still be asked to return postal votes in the European elections before 10 June.'
Councillor Barrett and his wife Moira were foster carers for their two grandchildren Christopher and Adam.
He spent his professional life working in housing and particularly with homeless people and other vulnerable groups. His career took him from Blackburn to Liverpool, London, Bolton and Blackpool.
As a councillor he held posts as chair of finance, vice chair of housing, and was lead member for resources.
His charity - united we stand, divided we fall - was raising money for vulnerable people in the borough.