Tickets for "The Park In Progress Tour" will cost £15 for adults, £10 for pensioners and students and £7 for children up to the age of 17. There are also special rates for groups of 10 or more.
London mayor and London Legacy Development Corporation chairman Boris Johnson described it as "a fantastic opportunity to relive our summer like no other and look ahead to an amazing summer series of concerts and sporting events".
The Park is set to reopen in phases from July, with concerts and sports events from the first anniversary of the London 2012 Games.
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The curtain will come down on the show for the final time at the Piccadilly Theatre in March next year, before embarking on a UK tour.