Days before he demitted office last month, Mukherjee had ordered setting aside of the penalty imposed on Kumar.
The HRD Ministry had last week issued orders to the IIT- Kharagpur Director to comply with Mukherjee's decision.
"I am directed to refer to the appeal dated September 3, 2014 filed by professor Rajeev Kumar and to say that the President of India, in his capacity as the Visitor of IIT- Kharagpur,...has set aside the penalty of compulsory retirement imposed on him," read the HRD Ministry order.
Kumar, when contacted, refused to comment on the issue.
IIT-Kharagpur had suspended Kumar for "misconduct" in May 2011 -- the same year the Supreme Court had lauded him as a "unsung hero" for his efforts to reform the IIT Joint Entrance Examination (JEE), which has since been re-christened as JEE Advanced.
He was accused of "damaging the reputation of the institute" by levelling allegations on issues ranging from irregularities in the purchase of laptops to rampant copying by students during examinations.
The institute set up a probe panel that found him guilty.
In 2014, the IIT decided to hand him compulsory retirement.
Kumar, who alleged that the panel was biased, moved the Delhi High Court and obtained a stay on the IIT's decision. He also appealed to the President requesting that the decision be quashed.
The appeal against the retirement order has been pending in the Delhi High Court.