The former Chippa United boss was brought in to replace Hunt, who has since joined Stellenbosch, with the team sitting comfortably in seventh place on the Betway Premiership standings.
After only lasting for a short spell with the Chilli Boys, Badela explained that he wants his new team to dominate opponents with exciting, expressive football.
He said on the club’s website: “I want a team that dominates the game, both with and without the ball.
“More importantly, I want the players to express themselves, play with energy, and work extremely hard on the pitch.””
City play Polokwane City on 25 January in their first game back after the Christmas and Africa Cup of Nations break.
“The team has done very well so far. My focus is on continuing that progress and helping the players fully express their strengths on the pitch,” Badela added.
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“We want people to enjoy coming to the stadium. We will give everything in every game and make Durban City an exciting team to watch.”