A raft of landmark agreements, including deals on ending long-running border disputes and sharing water from the Teesta river, are expected to be signed during the two-day visit.
Relations between the two South Asian neighbours have been marked by decades of mutual mistrust and low-level border clashes that have prevented the development of substantive trade and political ties.
The last visit by an Indian premier was in 1999 and Singh will be the first prime minister from India's Congress Party to visit in nearly 40 years.
"We attach the highest importance to further developing and strengthening our relations with Bangladesh," Singh said in a statement issued before his arrival.
"Our partnership with Bangladesh is important for the stability and prosperity of our own northeast region."
His trip comes after an embarrassing slip-up in June, when remarks by Singh claiming that many Bangladeshis were "very anti-Indian" were posted on his official website before being swiftly removed with the explanation that they were "off the record".
Nevertheless ties have improved since the traditionally pro-Indian Awami League party, led by Prime Minister Sheikh Hasina, swept to power in 2009 polls.
Last year India gave Bangladesh a billion-dollar soft loan, the biggest credit package New Delhi has ever earmarked for any nation.
"Singh's trip is an historic visit. It will pave the way for a prosperous future for the whole region," Bangladesh's Foreign Minister Dipu Moni told reporters on Sunday.
The two sides are to sign a key agreement to definitively demarcate their 4,000 kilometre (2,500 mile) shared border.
"There were many deaths and shootings on the border because we did not have a clear cut boundary," said Home Ministry official Kamal Uddin Ahmed, adding that Singh's visit will "comprehensively resolve all outstanding border issues."
As part of the deal, they will swap several hundred enclaves, tiny, landlocked communities in each other's territory, in which more than 50,000 people live, cut off from their respective governments and without access to even basic services.
The enclaves date back to ownership arrangements made centuries ago between local princes, and they survived the partition of the sub-continent in 1947 after British rule and Bangladesh's 1971 war of independence with Pakistan.
They are also scheduled to sign a water sharing agreement for a key common river, the Teesta, which would guarantee the flow of water to Bangladesh's most impoverished and water-starved northwestern districts.
However the signing has been put in doubt after the chief minister of West Bengal, the largest Indian state bordering Bangladesh, pulled out of Singh's delegation, saying the new treaty conceded too much.
"The subject is acknowledged as a very sensitive issue," Indian Foreign Secretary Ranjan Mathai told reporters on Monday.
"Nothing will be done without consultation with the state governments. Any agreement that we conclude will have to be acceptable to them and at the same time it has to be acceptable to Bangladesh."
India is currently seeking to improve ties with its close neighbours, partly in a bid to counter the growing regional influence of China, which is Bangladesh's largest trade partner.
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@Dr Priyanka, express your views if you can.. My dream is ahead then that. . .
@omg!: keep dreaming!
I do not agree with @rock. There is no future of India way long. The future is China, Central Asia and Middle East, for their way up growing economy and literacy. China is building highways in Central Asia and Pakistan. Turkey is becoming stronger with largest military of Europe, and self made weapons. Egypt got revolution. UAE getting skyscrapers, Saudi Oil and Irans Scientific is way too ahead then bunch of poor states of India. The future is not just one super power, but if yyou hav friendship with some potential powers too. India lacks. Just like USSR lacked during coldwar. " OIC and China is what NATO and US today...."
Thats whay India lacks --> Friends. They must do everything to please Pak
India loves every country that is against Pakistan i.e. Bangladesh. Or can be used against pakistan i.e. afghanistan and iran. But unluckily, by giving Dilai Lama asylum, they have made China there enemy. So the sword of threat that India has above their head, wud be on China, if ever India made Pakistan their partner just like China did. For me India is a buffer zone between Pakistan and China, and nothing else. Who evers conquer Delhi, Pak or China, the next target will be between us. India should give Kashmir to Pakistan for good ties. Even after Chahbar Port, Iran stands with Pakistan's stance of Kashmir.
@Rock, China has great relations with Central Asia too.. And because of friendship with Pakistan, it has opened 57 doors for China. An opportunity India missed. Live with your lone friend. God bless Bangala.
@Manna: World romances India you think about your country settle border dispute with India and afghanistan first. Bangladesh and india will live peacefuly. Progress is already made through border settlement and commission for water distribution.
@Manna: Are you confuse? Today even bangladesh hate jamat people. leave that issue it's between jamat and India. you better concentrate on your jamat people which i9s much more serious.
@Manna: Bangladesh is not concern about what pak says. Your country's role limited to trade as we are signing defence pact. Just wait for another SAARC summit.
@Manna: Read my sentence "China has very few neighbours as friend". Now today's homework for you is find out the neighybours of china and their border dispute with china.
@Rock: Haha .. China has few friends? In which world do you live? If they have few friends in its neighborhood then you have no friends at all. Reality is that a few days back your Govt , your media and establishment all three had been accusing Bangladesh and Its Jamat-e-Islami in particular and all Bangladeshis in general declaring them terrorists, You think they are going to forget that with the visit of your Dummy PM? Such things do not go away in 24 hours because your PM visits. Look who is your frien on East and West? That's enough for you to answer your own question. China is most liked nation even if compare with any other country in the world. Then compare that with India and You will see the picture clear. Bottom line is, China is preferred everywhere over India and specially in Indian neighborhood. Take a poll with Bangladeshis and you will see who they like China or India...You will clearly see it " CHINA"
@dictator: "It’s totally insane of manmohan to seek aid from Ex-Pak now named Bangladesh,"
It is unclear where you read that Manmohan Singh is seeking aid from Bangladesh So if you descibe Bangladesh as Ex-Pakistan, perhaps we should describe Pakistan as ex-India? Think before you write. Each of these 3 countries is sovereign and should be treated as such by any reasonable person.Pakistan should learn from bangladesh and try to resolve disputes with neighbours. Pakistan has 4 neighbours and has border dispute with 2 neighbours. India and afghanistan although you have gifted part of kashmir land to china.
China has very few neighbours as friend. Do you know why? Please ask them. :)
@ABC: Explain your statement... We will reply.
@Paras Vikmani: best friend or lone friend in South Asia?
We need progress in the region. jai hind, joy bangla!!
jai hind, joy bangla !!
We have to improve relations with Bangladesh which is our best friend in South Asia.