The handwritten account of Newton's eureka moment, which led to his famous theory of gravity, was recorded for posterity by the scientist's friend and colleague William Stukeley in a 1752 biography.
It is thought to be the first account of one of science's most famous anecdotes and the one that brought it to the general public's attention.
Until now the manuscript has remained hidden away in the Royal Society's archives - but from today anyone with internet access will be able to look at it.
It is one of a number of archive documents being published online by Britain's leading academic institution to mark its 350th anniversary.
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Lord Rees, president of the Royal Society - and Newton's modern-day successor - said: "Stukeley's biography is a precious artefact for historians of science and I am delighted that it is being made available today, along with other treasures from the archives, in a format that allows anybody to view them as if they were holding the manuscript in front of them."
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