As previously reported Klate had been in discussions with the Chilli Boys after seeing his contract out at The Clever Boys in June.
The club have since announced his arrival on a three-year deal, with the 33-year-old midfielder having been unveiled at a press conference in Port Elizabeth on Wednesday.
Chippa also swooped in on another former Wits midfielder in Jabulani Shongwe, who was previously being lined up by Maritzburg United.
The 28-year-old was on loan at Golden Arrows last season, and saw his contract with the Milpark-based outfit run out last month.
Also formally introduced to the media were former Mamelodi Sundowns defender Thabo Nthethe, Botswana internationals Thatoyaone Kgamanyane and Kabelo Seakanyeng, ex-Ajax Cape Town midfielder Ruzaigh Gamildien, as well as Tebogo Makobela from Jomo Cosmos, amongst others.
Re-appointed coach Dan Malesela has since outlined the club's intentions upon his return, highlighting their ambitions to attain silverware and compete on the continent in future.
"There are certain bonds that one just can't break, and I'm excited to be back at Chippa United FC," Malesela told the media.
"We were very careful with our selection [of signings] this season. We didn't only take the talent factor into consideration, we also looked at behaviour, age and a real want from the player to be at the club.
"I'm not going to make any promises about the upcoming season, but we are going to try our best. We'd like to compete on the continent, and win silverware."