The Togo international will spend the second of the campaign at the Soweto giants after being deemed surplus to requirements by Stuart Baxter.
Wome, who played for Mamelodi Sundowns and Free State Stars before joining Matsatsantsa, fell down the pecking order at the Tshwane giants.
He managed just eight appearances in all competitions under Baxter this season.
The 25-year-old will be looking to rediscover his old form at the Parktown-based club and help them return to the top half of the PSL log.
Wome's experience will be an added advantage to the Sea Robbers, who have not given up on challenging for the league title despite sitting in 10th position with just 18 points from 13 games.
He won the PSL title with Sundowns during the 2014/15 season.