@McTag,
There's a lot about this in Wikipedia.
An excerpt:
"The first sporting contest between the universities of Oxford and Cambridge was held on 4 June 1827, when a two-day cricket match at Lord's, organized by Charles Wordsworth, nephew of William, resulted in a draw. There is no record of any university "colours" being worn during the game.[1][2]
At the first Boat Race in 1829, the Oxford crew was dominated by students of Christ Church, whose college colours were dark blue. They wore white shirts with dark blue stripes, while Cambridge wore white with a pink or scarlet sash. At the second race, in 1836, a light blue ribbon was attached to the front of the Cambridge boat, probably as it was the colour of Eton. These colours — light blue for Cambridge, and dark blue for Oxford — became the official colours of the two boat clubs, and through the rivalry of the Boat Race, the colours became inextricably linked with the universities and contests between the two."