A statement on the Diocese of Gloucester website says Bishop Michael died peacefully at home on Monday evening, April 17, following a special Easter weekend with all the family.
Speaking in December last year, Rt Rev Michael Perham said he didn't expect to last another year.
His successor, Rt Rev Rachel Treweek, has paid tribute thanking him for his wisdom, insight and friendship.
Bishop Rachel says: "Amidst our pain and grief I am thankful that Bishop Michael died in this season of Eastertide when we celebrate Christ's power over death, and rejoice in the hope of resurrection and life everlasting. In his recent and final book 'The Way of Christ-likeness', Bishop Michael wrote The Christian who goes with Christ into the darkest places of Holy Week can also embrace a new life beyond imagining." This is true now for Bishop Michael who is with Jesus Christ."
Bishop Rachel continued: "I will always be grateful for Bishop Michael's wisdom, insight and friendship which I first experienced as a member of General Synod. It is an immense privilege to have followed in Bishop Michael's footsteps as Bishop of Gloucester and I am deeply aware of the significant impact of his ministry on the lives of individuals and worshipping communities across this diocese.
"Of course, his gifts and ministry have enabled and influenced so much beyond the borders of this diocese, not least in the prayers and liturgies of the Church of England. More recently Bishop Michael has also been an Honorary Assistant Bishop in the dioceses of Bath and Wells, Carlisle, Portsmouth and Salisbury."
She added: "As we give thanks for Bishop Michael we are also deeply thankful for Alison, and we pray for her and the family that they will know the everlasting arms of God beneath them and around them."
Bishop Michael's funeral will be in Gloucester Cathedral. The date and details will be made available once they are finalised.
(Image: Bishop of Gloucester)