Kenyan president Uhuru Kenyatta said Tutu's passing was "a big blow" not only to South Africa but to the entire African continent.
"Archbishop Tutu inspired a generation of African leaders who embraced his non-violent approaches in the liberation struggle," he said.
"A giant has fallen," wrote Uganda opposition leader Bobi Wine on Twitter.
"We thank God for his life -- a purposeful life, truly lived in the service of humanity. May his soul rest in peace. Condolences to all people world-over who were touched by his life and ministry."
Nelson Mandela Foundation
The foundation said the loss of Tutu was "immeasurable".
"He was larger than life, and for so many in South Africa and around the world his life has been a blessing.
"He was an extraordinary human being. A thinker. A leader. A shepherd."
Tutu and Nelson Mandela first met in the 1950s but did not see each other again for decades, on the day Mandela was released from prison in 1990. Mandela stayed at Tutu's home that night.
British prime minister Boris Johnson said he was "deeply saddened" by Tutu's death.
"He was a critical figure in the fight against apartheid and in the struggle to create a new South Africa -- and will be remembered for his spiritual leadership and irrepressible good humour," Johnson tweeted.
French president Emmanuel Macron said Tutu had "dedicated his life to human rights and equality between peoples".
"His struggle for the end of apartheid and for reconciliation in South Africa will remain in our memory," he tweeted.
Archbishop of Cape Town Thabo Makgoba said the life of Tutu, a "deeply spiritual person", should be celebrated.
"He named wrong wherever he saw it and by whomever it was committed. He challenged the systems that demeaned humanity."
European Council president Charles Michel offered sympathy to Tutu's family, President Cyril Ramaphosa and the South African people in general.
"A man who gave his life to freedom with a deep commitment to human dignity. A giant who stood up against apartheid. You will be deeply missed," he wrote on Twitter.
Jonas Gahr Store
Norwegian prime minister Jonas Gahr Store paid tribute to a man who "showed the power of reconciliation and forgiveness".
Highlighting Tutu's Nobel award, he added: "Never has a peace prize been so fitting."