He "died peacefully at home on Monday evening... following a special Easter weekend with the family", said the current bishop Rachel Treweek.
She added that she would "always be grateful for Bishop Michael's wisdom, insight and friendship".
Bishop Perham was cleared following two allegations of sexual assault in 2014. He later said the allegation had changed him "but I'm not sure how".
His funeral will be in Gloucester Cathedral, a statement said.
Bishop Treweek added: "I am deeply aware of the significant impact of his ministry on the lives of individuals and worshipping communities across this diocese."
The Diocese of Gloucester said that Bishop Perham would be remembered for his support of women bishops and known for his love of writing.
He was also later an honorary assistant bishop in Bath and Wells, Carlisle, Portsmouth and Salisbury.
But, during the last year of his tenure in Gloucester, he was questioned about two alleged sexual assault offences,  dating back to 1980 and 1981.
The Metropolitan Police and the Church of England carried out separate inquiries, both of which cleared him.
The former Bishop of Gloucester Michael Perham has died aged 69.