Cohen will now perform two shows on the same dates he was scheduled to perform at Hop Farm - but 75 miles away at London's Wembley Arena instead.
A statement on Cohen's website reads: "Due to unforeseen circumstances, Leonard Cohen's two shows at Hop Farm, Kent, on 8 and 9 September will no longer be taking place at that venue.
"However, Cohen will now be performing at a new London venue on the same dates.
"Cohen will still bring his much-anticipated Old Ideas World tour to the UK, with the scheduled shows now taking place in the fully-seated and historic Wembley Arena on 8 and 9 September."
Ticket holders for Hop Farm will be offered 'an exclusive pre-sale' for the Wembley dates, telling fans that Cohen's Wembley gigs will be his most "emotive, poignant and legendary concerts."
Organisers of Hop Farm have apologised to fans in statement.
"I would like to apologise to all the customers who have already bought tickets and hope they can still enjoy what are going to be two amazing shows at Wembley Arena," says organiser Vince Power.
Cohen's cancellation is likely to cause serious problems for the Hop Farm festival, which is yet to be confirmed for a 2013 return and was expected to return losses before Cohen cancelled.
Below: Leonard Cohen live gallery