"Presented PM @leehsienloong a reproduction of a map of the island of Singapore dating back to 1849," Modi tweeted.
On the second day of his bilateral visit to this city state, the Indian prime minister was hosted to a lunch banquet by Lee.
Modi stated that the map measuring 52 inches X 52 inches and based on a survey that was done during 1842-45, depicted topographical details of parts of Singapore.
"The map also depicts a description of various points in the vicinity of Singapore town above the level of low water spring tides," he tweeted.
"The reproduction was done from the cartographic collection of the National Archives of India, New Delhi," he added.
India and Singapore on Tuesday signed a joint declaration on strategic partnership and nine accords cutting across various sectors following talks between Modi and Lee.
After the signing of the documents, external affairs ministry spokesperson Vikas Swarup tweeted that the two prime ministers noted the importance of culture between the two countries and encouraged more exhibitions, exchanges and interactions.
Modi and Lee noted their shared interest in furthering cooperation in the areas of science and technology, particularly in space, biomedicine and ayurveda, the spokesperson added.
The two prime ministers also released two postal stamps showing Rashtrapati Bhavan and Istana, the Singaporean presidential palace, to mark 50 years of diplomatic relations between the two countries.
Earlier on Tuesday, Modi was accorded a ceremonial welcome at Istana following which he met Singapore President Tony Tan Keng Yam and Emeritus Senior Minister Goh Chok Tong.
Modi arrived in Singapore from Malaysia on Monday in the second and last leg of his four-day visit to southeast Asia.