He said Patel is a thorough professional with "impeccable integrity".
The Prime Minister said Patel leaves behind a great legacy and will be missed immensely.
"Dr Urjit Patel is an economist of a very high calibre with a deep and insightful understanding of macro-economic issues. He steered the banking system from chaos to order and ensured discipline. Under his leadership, the RBI brought financial stability," the PM wrote on Twitter.
"He has been in the Reserve Bank of India for about 6 years as Deputy Governor and Governor. He leaves behind a great legacy. We will miss him immensely," Modi said.
Meanwhile, Finance Minister Arun Jaitley Monday appreciated the service rendered by RBI Governor Urjit Patel saying it was a pleasure to deal with him and has benefitted from his scholarship.
"The Government acknowledges with deep sense of appreciation the services rendered by Dr Urjit Patel to this country both in his capacity as the Governor and the Deputy Governor of the RBI. It was a pleasure for me to deal with him and benefit from his scholarship," Jaitley tweeted.
"I wish Dr Patel all the very best and many more years of public service," he said.
Patel, who had a run in with the government over autonomy of the central bank, in a brief statement on Monday said he has decided to step down as RBI Governor with immediate effect. He, however, did not specify the reason for the decision.