The 30-year-old is a former teammate of the club’s head coach Benni McCarthy.
“I had other offers in Europe but this move was the right one for me, it feels great to return home playing again on African soil,” he told BBC Sport.
“But to play football to the fullest of your abilities, you have to be happy.
“So Cape Town City FC with its ambitions and objectives, as well as Cape Town as a city convinced me and my family to come over here.”
Obinna has already set his sights on winning the MTN8 with City after the team secure a final berth against SuperSport United.
“My targets are the same as the clubs target which is to challenge for the league and to win the finals of the MTN 8 trophy.”