His resignation has been received, Home Ministry sources told PTI.
The tenure of Joshi had expired a few months ago and he was sworn in again for another term.
But his resignation came a day after Union Home Secretary Anil Goswami called at least five Governors including K Sankaranarayanan of Maharashtra to put in their papers in the wake of change of government.
Though nothing has been officially disclosed, it is understood that other Governors who have been nudged to quit may include M K Narayanan (West Bengal) and Kamla Beniwal (Gujarat).
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Kerala Governor Sheila Dikshit, a former Delhi Chief Minister said she cannot comment on media reports.
Meanwhile, Rajasthan Governor Margaret Alva met Prime Minister Narendra Modi which was described as a courtesy call. She is also scheduled to call on the President Pranab Mukherjee.
Alva, who completes her five year term in August, is understood to have not been sounded out yet.
Karnataka Governor H R Bhardawaj, who like Beniwal did not share good rapport with the BJP government in the state, also called on the President today.
Patnaik, a former Congress chief minister of Odisha, said meeting the President, who is his friend, did not mean that he was resigning.