The warship's name has been linked to Leeds since the Second World War.
Today's Ark Royal is the fifth naval vessel to bear the name, but there are no current plans to build a replacement with the same identity.
Thousands of people took up the opportunity to board the ship, which has seen service in the Gulf War, and is expected to end its career with the Royal Navy in March.
It went into service in 1981, but its future is uncertain and it may be scrapped unless a buyer is found from an overseas navy.
Sailors from the Ark Royal performed a freedom of the city parade in Portsmouth on Saturday and are expected to do the same in Leeds next month.