Chippa last week recruited the Algerian fullback on a deal that will run until the end of the season.
The Chilli Boys have also added Linda Mntambo, Mxolisi Macuphu, Bantu Mzwakali and Thabo Rakhale to their roster in the January transfer window.
“He [Hachi] is a player that has played in the Champions League, and his experience will help us during the second round of the season,” Mpengesi told his club's website.
“His talent is not in doubt, despite not seeing much game-time at Mamelodi Sundowns.
“We welcome him in the blue and white of Chippa United and wish him all the best during his stay with us. He will get all the support for him to fulfill his potential.
“I would like to express my gratitude to Mamelodi Sundowns for the professionalism they displayed throughout the negotiations.”
Hachi, who has also turned out for ES Setif, believes the Port Elizabeth-based outfit are a team on the rise.
“Chippa United has evolved from last season, and you could see not only in the games against Mamelodi Sundowns but they have been strong this season,” he said.
“They have clear objectives to finish as high as possible on the league table and I am happy to make a contribution towards that.
“There is a lot of talent here; [Kurt] Lentjies, the midfielder Abel [(Mabaso], the winger on the left, no 7 [Paseka Mako] to mention but a few. Players with good energy always looking to attack.
“There is lot of quality and I will have to give my all to get the nod from the head coach [Teboho Moloi].”
Mid-table Chippa drew 0-0 with Golden Arrows on the weekend, and next visit fifth-placed Maritzburg United on Friday.