IIT Kharagpur had suspended Prof Kumar for "misconduct" in May 2011, the same year the Supreme Court had lauded him as an "unsung hero" for his efforts to reform the IIT Joint Entrance Examination (JEE) which has since been re-christened as JEE Advanced.
The institute had set up a probe panel that found him guilty.
Prof Kumar 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.
In 2014, the IIT decided to compulsorily retire him.
Prof Kumar, who alleged that the panel was biased, had moved the Delhi High Court and obtained a stay on the IIT's decision. He had also appealed to the then president requesting that the order be quashed.
Following the high court's stay order, Prof Kumar had taken lien for two years and joined Jawaharlal Nehru University in 2015. However, he was relieved from JNU in June to allow him to re-join IIT Kharagpur.
The IIT had last week accepted his resignation following communication of the Presidential order, and the professor had appealed to the JNU vice chancellor to reinstate him.
"Kumar will also be entitled to benefits from the date he was relieved from JNU," the official order said.
Days before he demitted office last month, Mukherjee had ordered setting aside of the penalty imposed on Prof Kumar.
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