Prasad, 26, arrived from I-League second division side Bhawanipore FC while Rajinder Kumar has been without a club since the end of the 2013-14 season of the I-League.
Both the players have already joined Bharat FC's pre-season training camp, the club said in a release.
Bharat FC will compete in its inaugural I-League season which kicks off on January 17.
Bangalore-born Prasad, son of former Karnataka state footballer P Jayaseelan and nephew of former international P Manoharan, began playing the game at the age of 10. He was part of the Sports Authority of India centre in Bangalore, playing for their under-19 team.
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Rajinder Kumar, a product of the Chandigarh Football Academy and son of a stone mason, has played for the India under-19 side. The 21-year-old was also part of the Pailan Arrows team in the 2011-2012 season.
The following season he transferred to Kolkata's United SC, making four appearances in the Federation Cup, scoring two goals. Kumar signed up with the Indian Super League but was not picked up in the domestic player draft.
Stuart Watkiss, head coach of Bharat FC, is of the opinion that Prasad's calmness in midfield coupled with Kumar's energy upfront was crucial to the team.