Victory over Namibia at the weekend ensured a 2-0 aggregate triumph for Amajita, leaving the team to wait to discover who their next opponent is.
Lesotho have been confirmed for the South Africans after they edged past Mozambique in their second-round tie.
Lesotho, nicknamed Makoanyane X, won 2-1 on aggregate after a 1-0 second-leg triumph at home and will host the first leg of their third-round tie against South Africa on either July 9 or 10 and play the return game away on either July 23 or 24.
The venue for the South African leg is still to be decided.
Lesotho have qualified previously for the continental championship in 2005 and 2011.
The winner of the tie joins hosts Zambia and six other countries in the championship scheduled for 26 February – 12 March 2017. The top four finishers then go to the U-20 World Cup in late May.