Fox-Pitt was injured when he fell from his horse Reinstated at the World Young Horse championships in France last October.
"I've come off a lot of times in my life, and in being knocked out my memory has been very selective and I've been able to put it behind me," he said.
He said the fall "affected my sight, my judgement and made me more dozy, in the beginning it was all a little bit of a dream. It's been an incredible journey, I've had incredible support."
In the jumping, London 2012 gold medallist Skelton again rides Big Star while Whitaker, who won silver in Los Angeles in 1984, will compete on Ornellaia.
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Whitaker's younger brother Michael, who also won silver in 1984, heads to his fifth Olympics on Cassionato.
As expected, the British Queen's grand-daughter Zara Tindall has missed out on selection for the dressage team. In 2012 she won silver but failed to make the shortlist this time.
Team GB was the most successful nation in equestrian events in 2012, winning three golds, one silver and a bronze across the three disciplines.
(Reporting by Alan Baldwin; editing by Ken Ferris and Clare Lovell)
