The amendment, according to a government official, paves the way for a person's extradition on the basis of a police warrant.
The official said an amendment to Article 10(3) of Bilateral Extradition Treaty between India and Bangladesh was signed in the presence of Indian Home Minister Rajnath Singh and his Bangladesh counterpart Asaduzzaman Khan Kamal on Thursday evening.
The Bangladesh Cabinet, chaired by Prime Minister Sheikh Hasina, cleared the amendment earlier this week.
The new provision requires no evidence to extradite a suspected criminal.
The amendment means handing over someone will require only the issue of an arrest warrant.
The deal previously required evidence before a suspect with a warrant out for him or her could be extradited for trial and a convict sent back home to serve a sentence.
During Thursday’s home ministry-level meeting, Rajnath Singh condemned the horrific terrorist attacks in Dhaka earlier this month and conveyed his deepest condolences.
He assured Bangladesh of India’s fullest support in its fight against terrorism, fundamentalism, and radicalism.
Singh said the two countries must always be vigilant to "defeat terrorism and ensure peace, security and prosperity".
He also welcomed the timely fulfilment of all commitments of the Land Boundary Agreement of 1974 and its Protocol of 2011 including the orderly movement of enclave dwellers choosing to move to mainland India, and completion of citizenship formalities on both sides.
Recalling the historic visit by Indian Prime Minister Narendra Modi to Bangladesh last year, the two home ministers agreed that it had infused a new dynamism in bilateral relations, widening the avenues for cooperation between the two countries.
During the talks, the two countries recalled Bangladesh Prime Minister Sheikh Hasina’s address in the wake of terrorist attacks in Bangladesh, emphasising the need for a united fight against terrorism.
Singh appreciated the various counter-terrorism measures taken by Bangladesh.
The two sides agreed to enhance cooperation between the security and investigative agencies of the two countries through training, capacity building, and exchange of information.
Both home ministers agreed on the need to immediately put into effect the Agreement on Combating Terrorism and Organized Crime and Illicit Drug Trafficking.
They also agreed to take urgent steps to repatriate released prisoners and victims of human trafficking.
India and Bangladesh emphasised the early execution of three bilateral MoUs to combat transnational crime at sea, prevent smuggling and circulation of fake currency notes, and fight human trafficking.
The two sides also stressed the effective implementation of the Coordinated Border Management Plan (CBMP) to increase cooperation between the border guards of the two countries to better monitor vulnerable areas and prevent border crime.