The change takes place at a time when Nepal is bracing for second elections of the Constituent Assembly in November.
During the meeting, Regmi praised the role played by Prasad while strengthening Nepal-India relations and described his tenure as Nepal's ambassador as highly successful.
"Regmi reaffirms that Indian role, companionship and support for the November polls is a key as his government is fully geared up to make it a success," said a statement issued by Regmi's office after the meeting.
Rae is from the 1980 batch of the Indian Foreign Service and has served as joint secretary (North), a division that oversees relations with Nepal, during 2002-2006 at the Ministry of External Affairs, at a time when Nepal was at peak of Maoist movement.
Rae, 56, is seen here as one of the architects of the 12-point agreement signed in 2005 in New Delhi between then seven-party Alliance of Nepal and the CPN (Maoist). The pact initiated the peace process in Nepal, got the Maoist rebels to join the peace process and made the first Constituent Assembly elections a reality.