After he took oath, Kovind was given a 21-gun salute to mark the assumption of office of the highest constitutional post in the country.
Once the oath taking was over, Kovind and Mukherjee exchanged seats on the dais after which the new president delivered his maiden speech as president.
Kovind was elected with 65 per cent of votes defeating Meira Kumar to occupy the top post.
The 71-year-old leader born in Kanpur, Uttar Pradesh, had also earned the support of the JD(U), which broke ranks with the "mahagathbandhan" because of his non-confrontational approach as governor of the state.
A commerce graduate, Kovind studied law at the Kanpur University, practised in the Delhi High Court and the Supreme Court. He was also the central government's standing counsel in the apex court from 1980-93.
Kovind, who headed Dalit Morcha from 1998 to 2002, also led the All-India Koli Samaj.
Elected to the Rajya Sabha in April 1994 from Uttar Pradesh, he served two consecutive terms till March 2006.
Outgoing Mukherjee bows out of public life after a five- decade political career.