"I resigned this morning and came to Shimla. I am relaxed now," Kumar said. (Agencies)
The resignation of 63-year-old Kumar came days after Union Home Secretary Anil Goswami had telephoned some of the Governors, appointed by the previous UPA regime, to step down after Narendra Modi-led government assumed charge at the Centre.
Uttar Pradesh Governor B L Joshi and Chhattisgarh Governor Shekhar Dutt had put in their papers last week.
Kumar, a former IPS officer who had served as Director of Central Bureau of Investigation, was appointed as Nagaland Governor in March 2013.
Kumar was CBI Director when the agency had arrested BJP general secretary Amit Shah in connection with the Sohrabuddin Sheikh alleged fake encounter killing case in Gujarat.
All the three Governors, who have resigned so far, are either former IPS or IAS officers. Joshi is a former IPS officer and Dutt is a former IAS officer.
However, no Governor with a political background has stepped down as yet.
Union Home Minister Rajnath Singh earlier in the day did not rule out the possibility of appointment of some new Governors before the Budget Session of Parliament beginning on July 7.
"I will not rule out anything now. I will be able to tell you only after 3-4 days," he said.
Sources said the government was considering appointing some BJP veterans as Governors in around ten states.
"I resigned this morning and came to Shimla. I am relaxed now," Kumar said.