The Belgian takes over the reins from caretaker co-coaches Lehlohonolo Seema and John Maduka.
Eymael, who quit City for 'private reasons', told Celtic's website: "I’m happy to join the team of such incredible stature with massive support. When I first arrived in the country, I somehow had a soft spot for the team purely because of the passion and dedication displayed by the supporters and trust me, I share the same thirst to win.
"My philosophy is simple, to play good football with appropriate tactical discipline. I have watched the team before and have seen some exceptionally good players that just need guidance and encouragement to start winning again."
Regarding the negotiations, Celtic's lawyer Mandla Tshabalala said: "I met with the coach in Johannesburg this morning [Friday] together with his representatives to discuss our interest in him and after an open meeting we agreed [just after lunch] and he committed towards joining the team."
Eymael will be in Rustenburg tomorrow to watch the team play Buya Msuthu in the Nedbank Cup.
Phunya Sele Sele are 13th on the topflight table with 18 points from 19 games - a point above the drop zone, and eight points shy of seventh-placed Rise and Shine.