Zungu was an influential figure at AmaTuks last season, helping the side finish in the top 8 on the PSL log with his exicitng attacking play.
Zungu joins an ever increasing list of new Sundowns players as the club continues to show its hand in the transfer market.
In other news, Bongani Khumalo is currently training at SuperSport United, in a bid to maintain his fitness before returning to Europe.
Khumalo will return to Tottenham Hotspur next season, with the hopes of breaking into the Andre Villas-Boas' first team.
In a report emerging from Soccer Laduma, Khama Billiat will join Lokomotiv Moskow for a trial, with the Russian club interested in acquiring the creative midfielder's services. The Ajax Cape Town player has been linked with a move to clubs in South Africa, but may jump at a chance to play for the Russian giants in Moscow.
The PSL will close the transfer season one day earlier at the end of this window, with the deadline set to move to the 30th of August.
"From our side, we are ready for the transfer window. As is normally the case we are expecting a slow start with activity increasing markedly as the deadline approaches,"PSL General Manager Derek Blanckensee said in a statement.
"Technologically our systems compare favorably with any others around the world and our staff are experienced in carrying out the necessary checks.
"What is important for us is to ensure that we process all the documentation for the players who will participate in the Absa Premiership fixtures on the opening weekend."