The ace badminton player defeated Malaysia's Tze Yong Ng for the title
The decision, taken during a board meeting last week, follows a disastrous South African World Cup campaign in which the Proteas finished seventh of the 10 teams.
The clean-out comes shortly before a tour of India next month during which South Africa will play their first three Test matches in the new world Test championship.
In a statement, CSA said a football-style team manager would be appointed, who would take charge of all aspects of the national team, including the appointment of a coaching staff, the captain or captains and medical and administrative personnel.
The team manager will report directly to a Director of Cricket, a new position.
Former South African player Corrie van Zyl, currently in charge of cricket pathways at CSA, will be acting Director of Cricket until a full-time appointment is made.
The statement said Van Zyl and CSA chief executive Thabang Moroe would appoint an interim management team for the tour of India as well as an interim selection panel and captain.
Faf du Plessis, the current captain, was on Saturday night named South African Cricketer of the Year and it would be a surprise if he was replaced.
Sunday's statement said none of the current team management, including coaches, would be retained.
"This change will herald an exciting new era for the SA cricket and will bring us into line with best practice in professional sport," said Moroe.
Former West Indian player and coach Gibson was appointed South African team coach in 2017. His contract was due to expire next month.
Gibson said during the recent Cricket World Cup that he was keen to continue in the job but his prospects plummeted when South Africa were among the first teams to be eliminated from contention for a World Cup semi-final place.
Van Zyl, 57, played in one unofficial Test during South Africa's years of isolation and in two one-day internationals in 1992 following the country's return to official international cricket. He had a brief spell as South African coach between 2009 and 2011.
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