Ndlovu, who plays for Qarabag FK from Azerbaijan, has been in fine form for the club and will join South African players such as Steven Pienaar, Benni McCarthy and Thulani Serero who have all played in the competition.
It will be a tough challenge for Ndlovu's Qarabag in group C, which also consists of Italian giants Roma and Atletico Madrid of Spain.
Coetzee's Glasgow Celtic side will take on Bayern Munich, PSG and Anderlecht in group B. It's a good opportunity for Coetzee to improve his game against some of the world's best players.
The 2017/18 Uefa Champions League draw was conducted on Thursday evening and defending champions Real Madrid will be looking to win the competition for a third consecutive time under the guidance of coach Zinedine Zidane.
Madrid, who beat Italian giants Juventus 4-1 in a one-sided final in Cardiff last season, have been drawn into group H with Borrusia Dortmund, Tottenham Hotspur as well as APOEL.
Europa League champions Manchester United make a return to the competition this season, as well as fellow English Premier League sides Chelsea and Liverpool.
Jose Mourinho's United side have been drawn into group A with Benfica, FC Basel and CSKA Moskva.
Group A: Benfica, Manchester United, FC Basel, CSKA Moskva
Group B: Bayern Munich, PSG, Anderlecht, Glasgow Celtic
Group C: Chelsea, Atletico Madrid, Roma, Qarabag FK
Group D: Juventus, Barcelona, Olympiakos, Sporting CP
Group E: Spartak Moskva, Sevilla, Liverpool, Maribor
Group F: Shakhtar Donetsk, Manchester City, Napoli, Feyenoord
Group G: Monaco, FC Porto, Besiktas, RP Leipzig
Group H: Real Madrid, Borussia Dortmund, Tottenham Hotspur, APOEL