The German Pentecostal preacher passed away "peacefully in his sleep" and "surrounded by loved ones" on Saturday.
His record-setting rallies drew crowds of millions, particularly across Africa where he spent 50 years sharing the gospel.
In 2000, 1.6 million people gathered in Lagos, Nigeria to hear him speak of God's healing power.
During his 60 year ministry Bonnke is said to have overseen more than 79 million Christian conversions and has been dubbed the "Billy Graham of Africa."
A statement from his family reads: "It is with sorrow that the Bonnke Family would like to announce the passing of our beloved husband, father, and grandfather, Evangelist Reinhard Bonnke. He passed away peacefully, surrounded by his family, on December 7, 2019."
The Bonnke family have offered their thanks to all those who have "enabled him to preach the matchless message of salvation to countless people" through their "kind love and unwavering support."
Journalist Peter Wooding attended his farewell crusade two years ago in Nigeria. He told Premier his "remarkable ministry" has inspired future generations to continue to fan "the flame of evangelism" he modelled so well.
Having interviewed him personally, Wooding recalled being struck by both his humility and relatability amid such influence.
Following his retirement in 2017, CfaN evangelist Daniel Kolenda was named his successor.
"Those who knew him off-stage can testify to his personal integrity, genuine kindness, and overflowing love for the Lord," Kolenda said. "His ministry was inspired and sustained by his rich prayer life, his deep understanding of the Word, and his unceasing intimacy with the Holy Spirit."
The family have requested mourners pay tribute to Bonnke's memory by donating to the ongoing work of Christ for all Nations - Africa Crusade.