He told the leaders 'the climate emergency comes down to a single number - the concentration of carbon in our atmosphere' and said they had a unique opportunity to stop that number rising any further.
"There's every reason to believe that the answer can be yes," he said.
The 95-year-old was among the opening speakers at the international climate conference, appearing in his role as the People's Advocate.
"In my lifetime I've witnessed a terrible decline. In yours, you could and should witness a wonderful recovery," he said.
Britain has cast the climate change summit in Glasgow as the last big chance to slow rising temperatures, and hopes to persuade leaders to adopt tougher climate targets.