With Warren Whiteley unavailable due to a knee injury, flanker Kolisi - who has 28 caps for the Springboks – will take on the role against Eddie Jones' men.
Pieter-Steph du Toit has been named as skipper for the preceding Test versus Wales in Washington on Saturday.
South Africa's director of rugby Rassie Erasmus said: "It's 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.
"I believe both of them will do a good job as captains.
Born in Zwide township near Port Elizabeth, Kolisi is also the DHL Stormers captain and has played in 28 Tests since making his debut at age 22 against Scotland in Nelspruit on 15 June 2013. He has four Test tries to his name. pic.twitter.com/I0bHXkHQSj
— South African Rugby (@Springboks) May 28, 2018
"My philosophy is that each player must take responsibility for his position and must therefore work extremely hard with that one goal in mind - to make the Springboks successful again."
Kolisi also captains the Stormers in Super Rugby and made his international debut against Scotland in Nelspruit five years ago.
Chiliboy Ralepelle was the first black player to captain South Africa, in a match against a World XV in 2006, but that contest did not carry Test status.
Erasmus has named a 26-man squad for the Test against Wales and will announce his starting line-up on Wednesday.
Photo Getty Images. Caption: Siya Kolisi in action for South Africa