During the visit, part of his policy to deepen engagement with India's immediate neighbourhood, Modi will hold wide-ranging talks with his Bangladeshi counterpart Sheikh Hasina on the whole gamut of ties and ways to move forward further.
Modi had earlier visited Nepal and Bhutan.
Ties between India and Bangladesh are on an upswing ever since Hasina government came to power in January, 2009.
Modi will be visiting at the invitation of Hasina who had extended the gesture through telephonic talk and writing a letter soon after Modi had led BJP to a landslide win in Lok Sabha elections in May, 2014.
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Earlier this month, Parliament had passed a historic constitution amendment bill seeking to settle India's 41-year-old border issue with Bangladesh. The bill will operationalise the 1974 India-Bangladesh Land Boundary agreement that provides for exchange of 161 enclaves adversely-held by the the two countries.
"This visit, Prime Minister's first to Bangladesh, reflects the importance attached by India to the bilateral relationship.
"The visit is expected to further expand the cordial and cooperative relationship between the two countries and strengthen the ties of friendship and trust between India and Bangladesh," the External Affairs Ministry said.
"Both the countries will give their approval to it very soon. We are hopeful that we will get full cooperation from West Bengal government", Singh said.
Last week, Bangladesh had hoped that the pact will be inked during Modi's trip.
The Teesta deal was set to be inked during the then Prime Minister Manmohan Singh's visit to Bangladesh in September 2011 but was postponed at the last minute due to objections by West Bengal Chief Minister Mamata Banarjee.
Modi's programme also include a meeting with Bangladesh President Md Abdul Hamid.
In March, 2013, President Pranab Mukherjee had paid a visit to Bangladesh.
Bangladesh is an important trading partner for India. The two-way trade in 2012-2013 was USD 5.34 billion with India's exports to Bangladesh accounting for USD 4.776 billion and imports USD 0.564 million.