The Serbian, who coached Botswana from 2002 to 2006 as well as Angolan outfit Interclube, has penned a two-year contract with Phunya Sele Sele.
Celtic CEO Khumbulani Konco has faith Jelušic can help the team bounce back from narrowly avoiding relegation in 2016/17.
He told the club's website: “We are honoured to have such a vastly experienced coach in our midst. Looking at how we performed last season, we are now solely focused on rebuilding the team. We are intending to give Coach Veselin sufficient time to assess and subsequently advise on where we need to beef up the squad during this pre-season. As much as positive results are important, we won’t be putting unnecessary pressure on our new man.
“He has worked with both youth and experienced players in the countries where he has coached and that will help us a lot. Luckily he has done research about the rich history of the team and he knows that the supporters are an integral part of the team. We welcome him and promise to give him all the necessary support so that we can all to achieve our goals.”
Jelušic has taken over the reins from caretaker boss Lehlohonolo Seema, who steered the side with John Maduka after the sacking of Serame Letsoaka in October last year.