Joshi, a retired IPS official had assumed charge as UP governor in 2009 during the second term of the Congress-led United Progressive Alliance (UPA) government.
Considered close to the Gandhi family, Joshi had put in his papers on Tuesday after the union home ministry sounded him on the subject.
Amid growing criticism on the subject of removing governors appointed by the predecessor government, state Bharatiya Janata Party president Laxmikant Bajpayi told IANS that there was nothing wrong in the developments.
"This is a 'swabhavik prakriya' (natural thing)" he said defending the reported move of the Narendra Modi government to seek resignation of over a dozen governors appointed by the last government. "I am very happy that B.L. Joshi has quit on his own," he added.
Many top veterans of the BJP are said to be in line to become governors.
Joshi, a retired IPS official had assumed charge as UP governor in 2009
The names doing the rounds include former Lucknow MP Lalji Tandon, former UP speaker Kesharinath Tripathi and former UP chief minister Kalyan Singh. All these state leaders were persuaded not to contest the Lok Sabha elections and are likely to be gratified by new postings in Raj Bhavans.
While Lalji Tandon, after initial diffidence, had vacated his seat for party president Rajnath Singh, now union home minister, Tripathi was denied a ticket from Allahabad and assured "adjustment later on".
Kalyan Singh, who left the BJP twice and floated his own regional outfit returned to the party in the run up to the Lok Sabha polls. A sitting MP from Etah, he was politely asked by Modi to make way for younger generation leaders and not to press for a second term.
He however was placated by being given a ticket for his son Rajveer Singh from Etah. He won. Kalyan is also likely to be made governor, sources said.