Botman died at his home in Stellenbosch on Friday night. He is survived by his wife, Beryl, and four children.
"Over the past few years Stellenbosch University benefited from his visionary leadership which portrayed his philosophy that SU's excellent research and teaching should make a difference in society," chairperson of the university council George Steyn said.
"He often asked me whether Stellenbosch University was doing enough to ensure that one day his and my grandchildren would be able to study here in Afrikaans," he said.
Steyn described Botman as a lovely and beloved person.
"I have great respect for his integrity and his leadership, among others for the manner in which he brought the then faculty of theology at the University of the Western Cape over to Stellenbosch University," he said.
Botman was scheduled to receive an honorary doctorate from the University of Aberdeen in Scotland in July, Steyn said.
"At the time of his death, he was also a serving director of higher education South Africa, senior vice-president of the Association of African Universities, chairman of the World Design Capital Cape Town 2014 Board and a director of Media24," Steyn said.
The Media24 board and management team on Saturday also expressed its sadness at Botman’s death.
“Professor Botman was a highly regarded member of our board whose quiet authority and sharp intellectual and philosophical insight into the role and strategic course of Media24 were deeply valued. On top of it, he was just such a lovely man. His death, so shortly after the passing of Professor Jakes Gerwel, our previous chairperson, comes as a double blow for Media24,” said Media24 CEO Esmaré Weideman in a statement.
Botman was born in Bloemfontein on 18 October 1953.
Senior lecturer in practical theology
In 1976, the year of the Soweto uprising, he led his fellow students in human rights protests against apartheid laws. He was ordained in 1982, he served as minister in the Wynberg congregation of the Dutch Reformed Mission Church from 1982 to 1993.
In 1994 he joined the University of Western Cape a senior lecturer in practical theology.
He became vice rector for teaching at the Stellenbosch University in 2002 and served in that position until his historic appointment as the institution's first black rector and vice-chancellor in 2007.
He also served as president of the South African Council of Churches from 2003 to 2007.
In 2010 he launched the University's Hope Project, a ground-breaking science-for-society initiative.
In 2013, he guided the university to the adoption of its new vision, which was to become more inclusive, innovative and future-focused.
In March he was awarded an honorary doctorate by Hope College in Michigan for leadership in higher education and the Reformed church to promote a more just society for all South Africans.
He received Princeton Theological Seminary's Abraham Kuyper Prize for Excellence in Theology and Public Life in April 2013.
Botman received honorary membership of the United Nations Association of South Africa for advancing the Millennium Development Goals.