The 24-year-old, who has been in contention for national selection for a while now after a string of impressive performances, got the nod in the squad after the national selectors preferred to go in with a young team.
The series will be held from July 24 to August 3 at Harare and Bulawayo.
The decision to rest Ravichandran Ashwin paved the way for Rasool's selection in the senior team since he is also an off-spinner.
The selectors also picked the India 'A' team for the tour of South Africa which also includes Rasool.
He has taken 46 wickets in 17 first-class matches and scored 1003 runs at an impressive average of 38.57.
Rasool was the standout performer for Jammu & Kashmir in the 2012-13 Ranji Trophy, ending the season as its top scorer and highest wicket-taker.
In his seven Ranji matches, Rasool scored 594 runs at 54 with two centuries, and took 33 wickets at 18.09 to finish as the third-highest wicket-taker among spinners in the tournament.