Nyatama was linked with a move to Pirates after making 28 PSL appearances for Phunya Sele Sele last season - netting five goals in the process.
The Soweto giants have since revealed that they have held successful talks with Celtic over the services of the 29-year-old player.
"The Club would like to thank Mr Max Tshabalala, Chairman of Bloemfontein Celtic, for the professional manner he conducted the negotiations.
"Nyatama, who hails from Benoni, is set to arrive in Johannesburg tomorrow together with his agent to undergo a medical."
Meanwhile, former Pirates midfielder Lehlogonolo Masalesa has joined Platinum Stars after deciding to return home following a short stint in Europe.
The 25-year-old player parted ways with Greek club Larissa at the end of last season - having joined the club in December, 2016.