The 15-cap forward won what was effectively a two-man race with another No. 8, Duane Vermeulen from French outfit Toulon, to succeed retired Adriaan Strauss.
"I am honoured and excited," said Whiteley after a 31-man squad was named by South African Rugby president Mark Alexander at a Johannesburg TV studio.
The under-pressure Coetzee hailed his new skipper: "Warren has been one of the outstanding leaders in South African rugby for many years.
"He is respected by his team-mates and opposition alike and has a lot of experience when it comes to captaincy.
"Warren has led the Lions with great authority for many seasons. He is resilient, copes well under pressure and makes good decisions."
Northern Bulls hooker Strauss quit following a calamitous 2016 season in which the Springboks lost eight of 12 Tests -- a calender year record for the team.
A nightmare first season in charge for Coetzee included conceding 57 points at home to New Zealand and a first loss to Italy.
Amid media speculation that Coetzee will be fired if South Africa lose the France series at home, he chose four foreign-based and eight uncapped players.
Vermeulen, Bordeaux prop Steven Kitshoff, Montpellier centre Francois Steyn and Worcester scrum-half Francois Hougaard are the South Africans playing abroad.
Steyn last played for the green and gold in 2012 and Coastal Sharks hooker Chiliboy Ralepelle returns after a three-year absence.
Full-back Andries Coetzee, wingers Dillyn Leyds, Raymond Rhule and Courtnall Skosan, centre Lukhanyo Am, scrum-half Ross Cronje and props Lizo Gqoboka and Ruan Dreyer have no Test experience.
South Africa play France in Pretoria (June 10), Durban (June 17) and Johannesburg (June 24)
South Africa squad
Forwards: Ruan Dreyer, Jaco Kriel, Malcolm Marx, Franco Mostert, Warren Whiteley (capt)(all Golden Lions), Eben Etzebeth, Siya Kolisi, Frans Malherbe, Bongi Mbonambi, Pieter-Steph du Toit (all Western Stormers), Tendai Mtawarira, Coenie Oosthuizen, Chiliboy Ralepelle (all Coastal Sharks), Lizo Gqoboka, Lood de Jager (both Northern Bulls), Steven Kitshoff (Bordeaux Begles/FRA), Oupa Mohoje (Central Cheetahs), Duane Vermeulen (Toulon/FRA)
Backs: Andries Coetzee, Ross Cronje, Elton Jantjies, Courtnall Skosan (all Lions), Jesse Kriel, Rudy Paige, Jan Serfontein (all Bulls), Damian de Allende, Dillyn Leyds (both Stormers), Lukhanyo Am (Sharks), Francois Hougaard (Worcester Warriors/ENG), Raymond Rhule (Cheetahs), Francois Steyn (Montpellier/FRA)