Razak has joined on loan after struggling for game-time in his first season at Chloorkop, while national U-23 international Likontsane has penned a three-year deal with Phunya Sele Sele.
The pair's arrival in the City of Roses will help offset the exit of Malawian hitman Hellings Mhango, who was recently let go after signing a pre-contract with Bidvest Wits.
"The new players will lift the pressure off our strikers and we trust that they will do the job at hand," Celtic CEO Khumbulani Konco told the side's official website.
"As a club, we welcome them and thank their respective teams on how they handled the negotiations."
Coach Serame Letsoaka has ample options upfront, with Helder Pelembe, Geofrey Massa and Lerato Lamola also among the recognised forwards at his disposal.