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.
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.