Home Ministry sources said the Governor has tendered his resignation.
80-year-old Narayanan was recently questioned by the CBI as a "witness" in the AgustaWestland VVIP helicopter deal probe.
The resignation came weeks after Union Home Secretary Anil Goswami had telephoned some of the Governors, appointed by the previous UPA regime, to step down after the Narendra Modi government assumed charge.
Nagaland Governor Ashwani Kumar, Uttar Pradesh Governor B L Joshi and Chhattisgarh Governor Shekhar Dutt have put in their papers in the last few days.
Narayanan, a former IPS officer who had served as Director of the Intelligence Bureau and was also the National Security Advisor, was appointed as the Governor of the state in January 2010.
All the four Governors who have resigned so far are either former IPS or IAS officers. Joshi and Kumar are former IPS officers while Dutt is a former IAS officer.
Sources said the government was considering appointing some BJP veterans as Governors in around ten states.