“He was [a] true South African patriot and treasure, whose loss is very deeply mourned,” he said in a statement.
“We send our most sincere condolences to his family. What an extraordinary man! May he rest in peace, and rise in glory.”
Tutu described Brink as a “gentle pathfinder whose stories coaxed his readers to challenge the racial enclaves in their minds” during apartheid.
Brink died on Friday night, aged 79, while on a flight from the Netherlands to Cape Town. He was returning from Belgium after receiving an honorary doctorate.
On Saturday, NB Publishers, which published all of Brink’s Afrikaans novels under its Human & Rousseau imprint, confirmed that the author had died.
Brink was a leading member of the Sestigers, a group of independent-minded Afrikaans writers who clashed repeatedly with the establishment.
His works were repeatedly banned, and he was an outspoken critic of censorship, which he said was being used in South Africa not to protect religious or moral beliefs, but as an extension of a repressive political apparatus.