West Bengal Chief Minister Mamata Banerjee also joined the inauguration through videoconferencing from West Bengal as the two leaders took part in the function from their offices in New Delhi and Dhaka.
This is the second train service launched between the two countries after the introduction of Maitree Express between Kolkata and Dhaka in 2008.
The three also inaugurated two bridges over the rivers Meghna and Titas in Bangladesh.
Modi was joined by External Affairs Minister Sushma Swaraj in New Delhi, while Hasina was joined by Bangladesh Foreign Minister A H Mahmood Ali and Minister of State for Foreign Affairs Shahriar Alam in Dhaka.
"I have always said that protocol must not come in the way of bilateral relations, especially when it comes to interactions with neighbors, and when it is aimed at achieving development and progress", Modi said.
The bridges will strengthen Bangladesh's rail network and "will help faster movement of both passenger and freight trains in Dhaka-Chittagong routes in Bangladesh", said a Railways Ministry tweet.
Hasina said that Bangladesh wants to cooperate with India and other neighbouring countries for creating a "peace area" in South Asia where all can live together as good neighbours and pursue constructive policies for the benefit of all.
Hasina said there has been an excellent relationship between Bangladesh and India and continuation of such ties is very much essential. "I'm sure these connectivity initiatives will further consolidate this vision".
The Bandhan Express will start ferrying passengers from November 16 onwards. "I look forward to working with you in our joint endeavour to that end". I hope the ties between the two countries deepen.
She said it was yet another happy occasion in Bangladesh-India relations.
The train has been named as "Bandhan Express" and it will operate on the 177-km-long Khulna-Kolkata route and the distance will be traversed within four-and-half hours.
Apart from Kolkata and Khulna, there will be two stops - Petrapole (in India) for around 10 minutes and Benapole (in Bangladesh) for around 15 minutes.
The 11-hour Kolkata-Dhaka journey via Maitree Express has two stops for immigration checking - one at Gede (Nadia) in India and the other at Dorshona in Bangladesh.
The two railway bridges have been built at a cost of $100 million, which has been met from India's $8 billion soft loan to Bangladesh.