Mathur, who was Chairman and Managing Director of Rajasthan Financial Corporation, succeeds TCA Ranganathan, who retired in November last year.
Anuraj Jain, a Joint Secretary in the Ministry of Finance, had held the charge as the head of the specialised export finance institution in the interim.
Mathur is an Indian Administrative Service officer from the 1986 batch and had worked with Golden Tobacco and cement major ACC before joining the IAS.
He was involved with the Exim Bank during his stint as assistant to the Executive Director of African Development Bank between 2001-03, the bank said in a statement.