Chungwa, who has been in fine form in the Zimbabwean Premier League this season, started training with City on Thursday after he landed in the country on Wednesday.
The Warriors striker was also named player of the month in the Zimbabwean Premier League in November. He finished the season as the top scorer in the league with 17 goals, but he could not inspire United to the title.
According to a source close to the player, Rise and Shine are working around the clock to register Chungwa in time for the league match against Mamelodi Sundowns at Peter Mokaba Stadium next Saturday.
"He is quality striker. He has been scoring a lot of goals in Zimbabwe this season," said the source.
"There were two other teams in the PSL that were interested in him but he opted to sign for Polokwane City."
Chungwa will compete with the league's top scorer Rodney Ramagalela and Walter Musona for a place in the starting line-up.