It was Military Secretary to the President, Major General Anil Khosla, inviting 71-year old Kovind and his wife Savita to the Rashtrapati Bhavan, where President Pranab Mukherjee was waiting for them in the study.
The two leaders then went to the grand Rashtrapai Bhavan forecourt where they were escorted to the saluting dais.
Mr Mukherjee took the last salute of the President's Bodyguard (PBG) with President-elect Kovind standing to his left.
The road from Rashtrapati Bhavan to Parliament was lined with jawans of the armed forces.
The morning had begun with the president-elect offering floral tributes to Mahatma Gandhi at Rajghat.