Varadarajan, who is currently Director (Finance) in BPCL, was selected by government's headhunter Public Enterprise Selection Board (PESB) in interviews held today, sources said.
He will replace RK Singh when he superannuates on September 30.
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Varadarajan, 56, will be the Chairman and Managing Director of BPCL till his superannuation at end of September 2016.
His candidature will now be vetted by the Cabinet Committee on Appointments headed by Prime Minister Manmohan Singh.