Here are the latest developments:
After shaking hands, the two leaders sat next to each other on a sofa, without delegates from either country around, and Mr Sharif was seen listening attentively as PM Modi spoke to him.
Details of the conversation were not immediately known, but government officials described it as a "courtesy meeting."
"Talks with PM Narendra Modi were good. Doors of dialogue should open," Mr Sharif said.
PM Modi and Mr Sharif had last held a formal meeting in Russia's Ufa in July this year, amid hopes of a thaw in ties.
But matters unraveled soon after with talks between the National Security Advisers of the two countries being canceled at the last minute over a meeting of the Pakistani envoy to India with Kashmiri separatists.
In September this year, both prime ministers attended the United Nations General Assembly in New York and even stayed at the same hotel, but did not hold a formal meeting.
Just minutes before a Summit on Peacekeeping was about to begin, however, Mr Sharif had waved at PM Modi, who had smiled and waved back.
After a brief pause, PM Modi had waved again to Mr Sharif, who had then smiled and nodded his head.
"The Prime Minister greatly values his relationship with Prime Minister Sharif and if they have waved at each other I don't see anything out of the ordinary in that," Ministry of External Affairs spokesperson Vikas Swarup had said then.
Mr Swarup first tweeted the picture today of the two Prime Ministers shaking hands and said, "PM @narendramodi meets PM Nawaz Sharif at COP 21 in Paris.