Known as massive open online courses (Moocs), the subjects covered include astrobiology and the search for extra-terrestrial life, artificial intelligence, philosophy and equine nutrition.
The courses are described as tasters for people interested in higher education but who are not in a position to enter it full-time. They have no entry requirements, run for five weeks (seven for philosophy) and are still open for enrolment.
University bosses said the 300,000 figure means there are now 10 remote learners online for each of the 30,000 students who attend the university.
Professor Sir Timothy O'Shea, university principal, said: "As someone who has researched in this area for more than 40 years, I am thrilled to bits that we have been able to attract so many learners to experience what Edinburgh has to offer. Online learning is an increasingly important method of teaching, opening up high-quality education opportunities to people around the world.
"I am delighted that these free courses have caught the imagination of the public and they also act as a great complement to our rapidly expanding efforts in providing other forms of online teaching, including full postgraduate and other distance-learning courses."