The agreement was signed in the presence of Finance Minister Jaitley and his Bangladeshi counterpart A M A Muhith after the two leaders held talks here.
"Bangladesh has developed significantly on the socioeconomic front in the past seven years," Jaitley said following the signing of the deal.
"We have stood by Bangladeshs attempts to develop and we will do so in the future. This significant agreement is a continuation of that effort," he said.
"They stood by us during our independence. We hope they will continue to do so in the future," Muhith said.
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The USD 4.5bn LoC was announced during Prime Minister Sheikh Hasina's visit to India in April.
Economic Relations Division Secretary Kazi Shofiqul Azam signed the deal on behalf of Bangladesh, while Managing Director of the Export-Import Bank of India (Exim) David Rasquinha signed for India.
The new Indian line of credit, worth USD 4.5 billion, will be used to fund 17 major projects in Bangladesh, which include electricity, railroads, roads, shipping and ports.
Under the agreement, Bangladesh would have to purchase 65 to 75 per cent of the services, goods or works from the Indian market with the money to be provided under the third LoC following the precedence of the previous two nearly identical agreements.
Bangladesh has two other LoCs open with India: the first one was signed in 2010, and the second one in 2016. These LOCs are collectively worth Tk3.06 billion, but till last year, Bangladesh government has been able to use only USD 576 million.