And this has raised hope for 70,000 people living in these 162 enclaves who are anxiously waiting for the implementation of the deal. They have lived there for years without the basic minimum facilities or even a clear national identity. But doubts about actual implementation still remain.
"An agreement has happened four times in the past too. Unless things change on the ground I am not convinced," said 44-year-old Mohd Aziz, a resident of the Mashaldanga Enclave.
The scepticism in his voice is hard to miss.
Aziz was born, and lives in Mashaldanga, a Bangladeshi enclave in West Bengal's Cooch Behar district, one of 51 Bangladeshi enclaves located within Indian territory.
Aziz lives here without a passport or any proof of identity, as does everyone else in his enclave. These people are Bangladeshi citizens who live on the lndian side of the border surrounded by Indian territory and no links to Bangladesh. The Indian government calls them foreigners and has not given them even the most basic facilities, like sanitation, electricity, water or education, and most importantly, an identity.
Across the border, there are 111 Indian enclaves within Bangladesh, where people are as desperate as those on this side of the border.
Historically, the enclaves are the result of a series of chess games between two kings in the area in the eighteenth century where villages were simply gambled away. After Independence, boundaries were drawn but the fate of these enclaves was never sorted out.
Manmohan Singh and Sheikh Hasina have agreed that Bangladeshi enclaves will become Indian territory and Indian enclaves will become part of Bangladesh.
"Identity is the most important thing for us, there is no doubt about that," said Diptiman Sengupta, Assistant Secretary, Bharat Bangladesh Enclave Exchange Coordination Committee.
The enclave exchange deal is good news for Jehad Hussain Obama. When his mother, a resident of the Bangladeshi Mashaldanga enclave, went into labour, doctors at a neighbouring Indian hospital refused to admit her. It was only after the entire village turned up at the hospital to protest that she was admitted and Jehad delivered. But the hospital refused to issue a birth certificate, saying that the infant was born to Bangladeshi parents.
The fight for the birth certificate is still on, but if the new deal is implemented, Jehad will have a clear identity and hopefully an easier life.