Officials said the decision to upload ceremonies on the website was aimed at reaching out to younger generation and people working in cyber space.
The move came two days after Mukherjee was sworn-in as the 13th President of the country.
The Rashtrapati Bhavan has already formed a page on the newly elected President on social networking site Facebook with a view to provide a platform for people to air their grievances.
The videos of two ceremonies including the President's meeting with the Chief Minister of Arunachal Pradeh Nabam Tuki has been put on Youtube, a Rashtrapati Bhavan official said.
People can view official ceremonies held inside the Rashtrapati Bhavan and give their comments on them.
"Soon, there will be more videos on the President's programmes. The aim behind such a move is to exploit online media to ensure better connectivity with the people in cyber world and keep pace with modern times to ensure fast dissemination of information," the official added.