The train is reviving a historic route that fell into disuse after the Partition.
At the launch, PM Modi said the "centuries-old historic bond between the people of India, especially from West Bengal, and Bangladesh, got a fresh boost."
Speaking in Bengali, he added, "I congratulate the people of the two countries on this auspicious occasion. Our ties of friendship got more strengthened today."
"Today is a great day for relations between the two countries... This train service is a dream come true for people on both sides of the border," Sheikh Hasina said.
Mamata Banerjee called it a "historic" occasion, not only for India and Bangladesh but also for "epar Bangla and opar Bangla" - a Bengali phrase commonly used to denote Bengali speaking areas divided by the border.
The 'Bandhan Express' will run once a week and cover a distance of 177 km in four-and-a-half hours. The service will begin from November 16. The air-conditioned train will have 456 seats.
Now, Maitree will take the same route as Bandhan, reducing the travel time to about 8 hours. Maitree runs houseful most days. It has 456 seats, the same as Bandhan.
Not just a new train, new immigration systems have been put in place to speed up the process. Earlier, passengers would have to get off the train with their luggage at the border station, walk through Customs and immigration and board the train again.
Now, an end-to-end Immigration and customs system is in place at station of origin and destination only.
"With these links, and today's projects, we have taken a few more steps in the right direction," the Prime Minister said.
The two premiers also inaugurated two rail bridges in Bangladesh that cost $100 million. Mr Modi said they would boost Bangladesh's rail network. "It is a matter of immense pride for India to be a trustworthy partner of Bangladesh," he added.
The Prime Minister had inaugurated several projects earlier through video-conferencing.
These include the South Asia Satellite in this May and, last year, the Integrated Check-Post (ICP) at Petrapole on India-Bangladesh border for cargo clearance to boost bilateral trade.