The white folk musician popularized the song by teaching it to a group of black activist students in 1960.
It was taken up as a rally cry and was sung at the 1965 march from Selma to Montgomery led by Martin Luther King.
President Johnson also quoted the lyrics when describing the Voting Rights Act of 1965.
The song has a long oral history and can be traced back to a 19th Century church hymn.
It has since been performed by Tiananmen Square protesters and at the dismantled Berlin Wall, the Times reported.
"Playing music at these kinds of situations, it wasn't just another form of entertainment," Carawan told the Chicago Tribune in 1990.
"It was sustenance for people going through hard times."
Carawan was born in California in 1927 and moved to New York City where he became active in the folk revival movement in Greenwich Village.
He and his second wife, Candie, taught music for decades at the Highlander Research and Education Center, a social justice leadership school in Tennessee. whose visitors over the years included Rosa Parks and Luther King.
Carawan had dementia and died at his home in Tennessee on Saturday, his wife told local media.
Guy Carawan, whose rendition of We Shall Overcome became an anthem of the US civil rights movement, has died at the age of  87.