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The multi-million-pound project also involves restoring peatlands in a bid to become carbon zero by 2040, and it plans to have zero emissions from heat and power by the same deadline.
Over an initial period of 50 years, by investing in tree planting and restoring peatlands in partnership with others, the university expects to remove almost 1.5 million tonnes of carbon dioxide from the atmosphere.
It is part of a package of recent measures such as removing investments in fossil fuels, a presumption against UK flights and investing in its own solar farm.
The university's internal research has indicated this approach to sequestering and storing carbon offers the best long-term value, as well as the most secure approach to meeting its own carbon commitments, when compared to other market-based carbon offset solutions.
Today's announcement begins a process that will allow the university to develop specific proposals and plans with partner organisations, with an aim of sequestering unavoidable carbon emissions in this way by 2024.
Principal and Vice-chancellor, Professor Peter Mathieson, said: "Taking climate change and loss of nature seriously is embedded in our strategy and our vision to make the world a better place.
"In making a multi-million-pound commitment, over an initial 50 years, we are uniting the University's cutting-edge climate research with our organisational commitment to take positive climate action.
"This announcement shows that universities can not only reduce our own impacts but that we can also play an important role as a positive force for change in the world.
"With the pivotal COP26 climate conference in Glasgow only weeks away, I am proud that the University has been able to take such a momentous decision to address our own carbon emissions and tackle the natural crises, and I hope this will act as a beacon for others in the higher education sector and beyond."
Scottish Environment Protection Agency(SEPA) Chief Executive, Terry A'Hearn said: "Humanity has a decade to save itself from the worst of the climate emergency by acting at scale and pace to reduce carbon impacts.
"Every organisation in every sector needs to step up.
"This commitment here from the university is exactly what we need - clear action and, importantly, ones that try to create additional benefits by being built into the University's core education work.
"SEPA applauds the university for this plan and looks forward to supporting its implementation where we can."
Francesca Osowska, Chief Executive of NatureScot, said: "The nature loss and climate change crises are inextricably linked, and with this ambitious and innovative project, University of Edinburgh strengthens its status as an educational world leader.
"We advised on this inspiring project and hope it is just the beginning for universities and many other organisations to find new ways to work together, combining expertise to tackle some of the most pressing issues we currently face.
"We hope that many other universities will see this project as a success story they can emulate, and an important way forward in bringing substantial benefits to local communities, learning, the state of nature and reducing carbon emissions."