The agreement was signed by Chinese Foreign Minister Wang Yi and Kamath at a special ceremony, which was attended by RBI Governor Raghuram Rajan and IMF chief Christine Lagarde.
The bank also signed a separate Memorandum of Understanding (MoU) with the local Municipal government headed by Mayor Yang Xiong.
The agreements accord legal status to the NDB under the Chinese regulations to function from the country.
Indian Ambassador to China Vijay Gokhale also attended the ceremony.
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"Today's agreements related to our Headquarters in Shanghai are a landmark step in our nascent journey as a development bank. With this we are now ready for business and we look forward to building an institution of repute in the course of time," Kamath said.
The bank commenced operations with an initial subscribed capital of USD 50 billion with total paid-in capital of USD 10 billion. The founding members of the NDB have already brought in capital of USD one billion as initial contribution.
The new bank will start issuing loans to green energy ventures and infrastructure projects from April this year.