The attacker was spotted at Naturena on Thursday, and he trained with the rest of the first team in the morning.
Kaizer Chiefs (@KaizerChiefs) July 27, 2017
Zuma's signing comes two days after Steve Komphela said Chiefs were done in the transfer market.
He becomes the club's fourth signing in the current transfer window, following the arrivals of Teenage Hadebe, Philani Zulu and Bhongolethu Jayiya.
The 22-year-old made 19 appearances for Phunya Sele Sele without finding the back of the net.
However, he registered two assists to his name in a season which was very difficult for the Free State club.
The Pietermaritzburg-born expressed his delight after putting pen to paper with the Soweto giants.
“It’s a great feeling to be at Chiefs and to have trained with the squad for the first time this morning,” Zuma told the Amakhosi website.
“My whole family supports Kaizer Chiefs. My parents, my one brother, my grandmother and my aunt,” he said.
Zuma said he grew up looking up to the likes David Mathebula and Gert Schalkwyk, and he intends to emulate the duo in the next three years at Amakhosi.
He also aims to help Chiefs win trophies in the upcoming campaign. Chiefs have not won a major trophy since 2015.
“I loved above all Mathebula and Schalkwyk, because they used to create chances to make the team play. That’s what I like to do as well,” he explained.
“I promise the supporters that I want to help Chiefs win trophies this coming season,” concluded Zuma.