In separate letters to Mukherjee, President M Zillur Rahman and Prime Minister Sheikh Hasina wished him a successful tenure at the highest office of India.
Hasina also called up Mukherjee congratulating him on his election and described him as a "time-tested good friend striving hard to elevate" India-Bangladesh relations to an "enviable level".
They expressed hope that Bangladesh-India relations would grow further "under your direction".
Hasina expressed happiness over Mukherjee becoming the first Bengali to hold the highest office of India.
She said "well-deserved election of Pranab Mukherjee as the President of India "bears the testimony to trust and confidence which the political leadership and the people of India reposes in him.
"It's also the recognition of vast experience and knowledge that you have gained over the last 50 years in your politics for the people."
More From This Section
Pointing out that Bangladesh attaches the highest importance to ever strengthening the bonds of friendship with India, the Prime Minister said "since our government assumed office in January 2009, it has been an endeavour to explore new opportunities to realise mutual benefits for our two countries and peoples."
She hailed Mukherjee's personal efforts for attaining the same "as a great source of inspiration".
Recalling Mukherjee's steadfast support extended to the people of Bangladesh "during the days of struggle for the country's independence in 1971", Hasina said "since then, your association with Bangladesh and her people has been of a time-tested good friend striving hard to elevate our two countries' relations to an enviable level."