Their teams, which will be selected in the coming weeks, will don the institutions' distinctive sporting colours to race on horseback at Newmarket in front of a crowd of 10,000 people.
The race will take place in October over eight furlongs on the course's Rowley Mile, with five riders competing from each university.
Two prizes will be on offer: one for the jockey who is first past the post and one for the university whose riders place better overall, The Telegraph reported.
The horseracing industry said the event had "captured the imaginations" of both universities, with the number of students applying to compete in the race exceeding the number of places available.
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The final five riders for each of the institutions will be chosen in early October.
Great British Racing said that while both Oxford and Cambridge have active equestrian clubs this will be the first time they have faced each other on a racecourse.
The riders from Cambridge will be wearing silks in the light blue worn by their rowing team, while those from Oxford will be wearing the dark blue used by their boat club.
Beckett said: "I've spent two years trying to get this race off the ground so I'm delighted to see it come to fruition. Fingers-crossed it will become an annual event, enabling riders to qualify for a Blue in future years."
A spokesman for Great British Racing said: "There is already quite a keen rivalry. There is every intention to do it every year.