The Zimbabwean striker's future had been a subject of speculation in recent weeks as he was linked with a possible move to Chippa United, but Rise and Shine have won the race for his signature.
Ezenkosi announced the move on Thursday afternoon as they wished the former Highlands Park hitman the best of luck at his new club.
Mashumba joins Zimbabwean teammates such as George Chigova and Walter Musona at Polokwane City.
Although Mashumba was one of the most prolific strikers in the NFD where he netted 17 goals for Cosmos in the 2014/15 season, he could not continue with his goalscoring form in the top tier at the Lions of the North.
Mashumba will now aim to use this opportunity at City and impress coach Jozef Vukusic.
He will compete with the likes of Rodney Ramagalela, Musona and Mohammed Anas among others.
City will be in action this weekend against AmaZulu and Mashumba will hope to feature.