Court members agreed the changes will be completed within a timescale of three years.
Since 2010, the University has invested more than £150 million ($209.4 million) in low carbon technology, climate-related research and businesses that directly benefit the environment.
The University of Edinburgh has the largest endowment fund of any university in Scotland. It will now become the largest university endowment in the UK to be free of fossil fuel investment.
In May 2015, the University signaled its intention to use its investments and procurement power to support the transition to a low carbon economy and to divest from the most polluting fossil fuel companies.
In 2013, Edinburgh became the first university in Europe to become a signatory to the Principles for Responsible Investment, a UN-backed initiative which aims to make the global financial system more sustainable.
Investment in fossil fuels currently represents less than 1 percent of the total University of Edinburgh funds under management, which is around £1 billion ($1.4 billion).
Ollie Glick, Edinburgh University Students' Association's Vice-President Community said “We are delighted with today's announcement. Students and the Students' Association have been passionate about removing fossil fuel investment from the University‘s portfolio for many years.”