The 26-year-old flanker will be the Springboks’ first black Test captain in the three-game series against Eddie Jones’ side in June.
Kolisi, who has played in 28 international Tests, replaces the injured Warren Whiteley as skipper.
Pieter-Steph du Toit will take the armband when Rassie Erasmus’ side take on Wales in Washington DC on Saturday.
Head coach Erasmus said: “I believe both [Kolisi and du Toit] will do a good job as captains.
“It is a huge honour to captain the Springboks and Siya and Pieter-Steph are two honest, hard-working men who enjoy the respect of their fellow players.”
Kolisi, who captains Super Rugby side Western Stormers, is not the first black player to captain his country.
Chiliboy Ralepelle led the Springboks in a match against a World XV in England in 2006, but that match did not have Test status.
Black players were banned from playing rugby during apartheid in South Africa.
Both the country’s government and South African Rugby have agreed that 50 per cent of the Springboks team at the 2019 Rugby World Cup in Japan should be black.