The Venezuelan is the third signing Sundowns have made, following the arrivals of Toni Silva and Bafana Bafana midfielder Andile Jali.
Meza will join fellow South Americans Gaston Sirino and Ricardo Nascimento at the club.
Like Sirino, Meza was playing his football in Bolivia for Oriente Petrolero and a lot will be expected from him, considering how well his fellow South Americans have performed since joining Sundowns in January.
The arrival of Meza and Silva means Sundowns will have to let go of two of their foreign players. Word is that Bangaly Soumahoro and goalkeeper Razak Brimah could be sacrificed by coach Pitso Mosimane.