The 35-year-old skippered the Proteas in 112 international matches since taking on the role in 2012, scoring 5,101 runs including 11 centuries.
He said: “The last few weeks of rest away from the game have given me a lot of perspective on the great privilege and honour I have had in representing and leading my country in the three formats of this wonderful game.
“It has been a rewarding, sometimes tough and other times a lonely road, but I would not replace the experience for anything, because it has made me the man that I am proud to be today.
“When I took over the leadership, I did so with the commitment to lead, perform and most importantly, to serve.
“As the team heads into a new direction with new leaders and a young crop of players, I feel it will be in the best interests of South African cricket to relinquish the captaincy in all formats.
“This was one of the toughest decisions to make, but I remain fully committed to supporting Quinton, Mark (Boucher) and my team-mates as we continue to rebuild and re-align as a group.
“I have strived to lead the team with dignity and authenticity during exhilarating highs and devastating lows. I have given my everything during my tenure.
“I have never been one to throw in the towel and do believe I am putting the team first and believe we have to stick through the tough times to get to the good times.”
Bairstow and Mike Cowan were named vice-presidents.
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SBR is constantly updating the situation with regards to world Cricket and all the competition statuses with regards to the repercussions
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English season delayed by at least seven weeks.