Desmond Haynes, West Indies' lead selector, said: "Athanaze is one of the young players who we have invested in, and he played well in the A Team and CWI President's XI.
"He showed great promise in the CG United Super50 last year and then got his first hundred in the West Indies Championship last week. We believe he should be given an opportunity at this level. He has also showed leadership, as captain of the Windwards at the start of this season."
Jordan, 28, has only played five games in his first-class career but is the leading wicket-taker after two rounds of the regional championship this year, with 12 scalps at 16.58. Jayden Seales remains unavailable following knee surgery and Anderson Phillip is not yet match fit.
"Jordan has been very impressive from last year," Haynes said. "He has continued to bowl well, and has been excellent in the first two matches so far this year. He is very skillful, can bowl the new ball, and looks to put the ball in the right areas. He is also a sharp fielder and good catcher close to the wicket."
West Indies arrive in South Africa on Friday, three days after Gudakesh Motie's 13-wicket haul helped them to an innings victory over Zimbabwe in the second Test in Bulawayo. They play a warm-up match in Benoni (February 21-24) before Tests in Centurion (February 28-March 4) and Johannesburg (March 8-12), with three ODIs and three T20Is following from March 16-28.
"This will be a challenging tour," Haynes said. "There is no easy away tour in Test cricket. South Africa have a good team, but I am sure we will be up for the task and will do well in these two Test matches."
West Indies squad to play South Africa: Kraigg Brathwaite (captain), Alick Athanaze, Jermaine Blackwood, Tagenarine Chanderpaul, Roston Chase, Joshua Da Silva, Shannon Gabriel, Jason Holder, Akeem Jordan, Alzarri Joseph, Kyle Mayers, Gudakesh Motie, Raymon Reifer, Kemar Roach, Devon Thomas.