The parade commemorated King Charles II's founding of the institution in 1681.
Founder's Day is also known as Oak Apple Day, which refers to the oak tree that Charles hid in to avoid being captured by Parliamentary forces after the Battle of Worcester in 1651.
Prince Harry, a former Army officer, arrived at the event wearing his Blues and Royals frock coat and like all the pensioners and guests wore a sprig of oak leaves in honour of Charles.
Speaking at the Founder's Day ceremony, the Duke of Sussex said he was 'honoured' to be able to attend such an event on the 75th anniversary of D-Day.
"Not only is today a prominent historical occasion, it is also a special day in the Royal Hospital calendar - bringing together families, old friends and the chance to make new ones," he said.
Standing before the crowd at the Royal Hospital, he said the men were also 'seriously good fun to be around' and recommended them never to 'ever underestimate the joy that you bring to everyone [they] meet'.
"I see a community that continues to value the importance of teamwork which military service in particular can teach you."
Meanwhile, the Duke of Cambridge attended a service of commemoration at the National Memorial Arboretum marking the 75th anniversary of the Normandy landings.