The scientist studied climate change for decades and wrote a number of books charting its effects on wildlife and ecosystems in the US, and later chronicled its effect on the nation's politics and policy.
"A prolific researcher and author, co-founder of the journal Climatic Change, and a wonderful communicator, his contributions to the advancement of climate science will be sorely missed," Mr Gore said.
Mr Schneider was an influential, and at times combative, public voice in arguing the man-made causes of climate change and appeared on news and science television programmes, wrote articles and blogged.
"Through his books, his extensive public speaking, and his many interactions with the media, Steve did for climate science what Carl Sagan did for astronomy," said Ben Santer, a climate researcher at the Lawrence Livermore National Laboratory.
As a co-author of the Intergovernmental Panel on Climate Change reports that earned a share of the Nobel, Mr Schneider defended the panel's work when it came under attack from critics after some unsettling errors were discovered, including how fast Himalayan glaciers were expected to melt.
The errors were made in a subsection of the world's most authoritative report on global warming and were found to be insignificant to its overall findings that glaciers are melting faster than ever.
"Steve, more than anything, whether you agreed with him or not, forced us to confront this real possibility of climate change," Jeff Koseff, his colleague at Stanford's Woods Institute for the Environment, said.