The academic was the founder of of L'Arche, an organisation described as a revolutionary international network of communities where people with and without disabilities live and work together as peers.
"Jean has left an extraordinary legacy," L'Arche international leader Stephan Posner said in a statement.
"His Community of Trosly, the Communities of L'Arche, Faith and Light, many other movements, and countless thousands of people have cherished his words and benefited from his vision."
Mr Vanier, who was a Catholic, founded L'Arche in 1964 in response to the treatment that people with learning disabilities faced in institutions.
He spent a lifetime reshaping society's views on the value of disabled people and was recognised for his work.
In 2015 he was awarded the Templeton Prize, picking up a cheque for £1.1 million.
We are deeply saddened to announce the passing of Jean Vanier. He passed away peacefully today Tuesday, May 7 at 2:10 am in Paris surrounded by some relatives. https://t.co/74rYPjpB2Vpic.twitter.com/F9MhZ2F9oY— L'Arche International (@larcheintl) May 7, 2019
Shortly after nomination of the prestigious prize, he told Premier how he sees Jesus in the daily life of the community he built: "It's a question of loving people as they are.
"Not just people with disabilities but also the assistants [L'Arche's volunteers].
"The whole vision of Jesus is just to 'love one another as I have loved you'.
"To love people is not to do things for them, but to reveal to them that they have value. There's a person under the abilities and the disabilities - that's the heart."
There are now more than 150 L'Arche communities in 38 countries around the world, where more than ten thousand people share in life together.
John Sargent, National Leader of L'Arche UK, said: "Jean's death is a great sadness. His vision was one of radical welcome, inclusion and joy, where marginalised people with learning disabilities are valued and celebrated.
"He will be greatly missed by people from all walks of life who have been influenced and changed by his teachings, which remain as relevant today as ever."
Mr Vanier spent his life after retirement from L'Arche focusing on "sharing a message of unity, dignity and diversity".
He influenced thousands of people around the world and published forty books on how people with learning disabilities contribute to building a more humane society.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.