The news were broken by Teko Modise on his Instagram account on Wednesday without revealing where the two players will be plying their trade next season.
The veteran midfielder, who has been with City for a season now, wished his soon-to-be former teammates well in their future endeavours.
Gumede and Kobola have been with the Citizens since 2016, and they both played a huge role in ensuring that the club becomes the big brand it is today.
While Modise did spill all the beans, reports suggest that Gumede could be on his way to Kaizer Chiefs, while Kobola's next destination is still unknown.
Chiefs promised to make changes to their player personnel ahead of the next season, but whether or not they are looking to bring in Gumede remains to be seen.
The departures of Gumede and Kobola would be seen as a massive blow for City, who will be without skipper Robyn Johannes next season. Johannes is on his way to Bidvest Wits.
In recent months, City lost several of their key players, including Lebogang Manyama and Aubrey Ngoma.
They will now have to reinforce their defence ahead of next season with three of their regular players now on their way out of the club.
Benni McCarthy's future at the Mother City-based side is also up in the air with latest reports in the media suggesting that Amakhosi have began to ask questions about his availability.
The 40-year-old mentor only joined City at the start of the 2017/18 season following Eric Tinkler's departure to SuperSport United.
He did fairly well in his first season in charge as he guided the club to the MTN8 final where they lost to eventual winners SuperSport Unted.