The Duchess wore a teal green coat and a black fascinator while the Queen opted for a bright pink Angela Kelly outfit.
As the royal party walked through The Magazine - one of the ancient gates to Leicester - they were greeted by dancers and city dignitaries.
Crowds 20 or 30 deep were packed behind the barriers which surrounded the main entrance of the modern university building.
The Queen arrived first to loud cheers which got louder as the Duchess walked into the square. She paused to wave and smile at the crowd.