Mr Rodney founded Crystal Cruises where he has been president since 1987. Before then, he was president of Princess Cruises.
Disney aims to set sail in 1998 with ships capable of carrying 2,400 passengers in state rooms, family suites and luxury state rooms.
Disney's cruises will be a week long, with three or four days at sea and the remainder of the week at Walt Disney World Resort in Florida. The cruise will also offer, as a port of call, one day at a private island owned by Disney.
Cruises will include activities featuring Disney characters for families. All age groups will be catered for.
The cruise holiday has become a top money-spinner for US holiday companies, which have done particularly well in the Caribbean. Load factors on ships operating there seldom dip below 100 per cent.
US cruise holidays cost around dollars 1,000 (pounds 650) a person for 10 days - less than half the average pounds 1,500 spent by Britons.
Last week, Airtours, the UK's second-largest holiday company, bought its first cruise ship and said it aimed to bring the American experience to the Mediterranean, which suggests it will undercut rival operators.Reuse content