The highly-rated forward joined the Buccaneers from Zambian Super League side Nkwazi FC this week.
According to Daily Sun, Shonga signed for Sundowns during the 2017 Cosafa Cup held in the North West Province in July.
Shonga was one of Zambia's star players as they reached the Cosafa Cup final where they lost to Zimbabwe.
The 20-year-old is said to have signed a three-year contract with an option to extend for two-years with Downs reportedly paying a deposit in the process.
After they had reached their foreign quota for this season, Downs were going to loan him back to Nkwazi and then take him back during the January transfer window.