The defender-come-midfielder has asked the distressed club to release him amid interest from the Buccaneers.
Phunya Sele Sele confirmed that they had terminated Ndengane's contract with immediate effect.
A club statement reads: "After some lengthy yet cordial discussions with Alfred Ndengane’s representatives, Bloemfontein Celtic has finally agreed to release the resolute defender from his contract. The versatile and humble defender will as from 1st of October, 2018 not be part of the team."
Celtic CEO Khumbulani Konco stated that there was no bad blood between the player and the Free State-based outfit.
“It is incredibly painful losing a player of Ndengane’s calibre. However, after speaking to him for months trying to convince him to stay, we realized he was adamant about his request to be released," Konco said on the club's official website.
"I must emphasize though, that through negotiations for him to extend his stay and his ultimate decision to depart, there was no bad blood but rather amicable discussions through his manager," he continued.
“We therefore wish him all the best in his future endeavours and wholeheartedly, thank him for his professional conduct and contribution towards the brand Celtic," he concluded.
The 31-year-old player has been one of the top performers this season and he was named PSL Player of the Month for the month of August after helping Celtic win their first three league games.
Ndengane was heavily linked with a move to Pirates last season, but Celtic managed to retain his services.
Recent reports have indicated that Bucs have renewed their interest in the experienced player, who is now a free agent.