The church confirmed Mr Monson died at home in Salt Lake City, Utah, surrounded by his family.
He had spent more than five decades serving in top church leadership councils.
In a statement on its website, the Mormon church paid tribute to a leader who “had all the hallmarks of an unassuming servant of the Lord”.
As head of the Church of Jesus Christ of Latter-day Saints – as the Mormon religion is officially known – Mr Monson led a global membership of 15.8 million.
He became a church bishop at just 22 years old, before entering its highest echelons at 36, as the youngest ever member of the Quorum of the Twelve Apostles.
The Salt Lake City native served as a counsellor to three church presidents before assuming the role of president in 2008.
He led the church for nine years before his death.
Mormonism is one of the world’s fastest-growing and most affluent religions.
Its followers worship Jesus and believe in a “restored” church with living apostles and prophets.
They also believe in an additional testament to those found in the traditional Bible, known as the Book of Mormon.
The president, counsellors and the 12 apostles are all considered to be prophets who receive divine revelations directly from God.