Following on from his previously-announced show at Hop Farm in Kent, Cohen plays a second show at the same venue on the next day, Sunday, September 9.
Organiser Vince Power said: "The demand has been overwhelming and it's fantastic to announce the extra date.
"These will be Leonard Cohen's only UK dates this year and we're over the moon he's decided to play them here. It promises to be a fantastic weekend."
Tickets go on sale this Monday, May 21, though members of Cohen's fan club will have access to a pre-sale from tomorrow (May 18). They are priced at £65 and £85.
The two-day event in Paddock Wood follows the annual Hop Farm Festival at the same venue, which takes place in June and July.
This year's Hop Farm Festival is headlined by Bob Dylan, Suede and Peter Gabriel and the New Blood Orchestra, with support from Damien Rice, Primal Scream, My Morning Jacket, Maximo Park, Patti Smith, Bruce Forsyth and more.
Cohen this year released his 12th studio album Old Ideas, his first since 2004's Dear Heather.
Watch the Leonard Cohen 'Show Me The Place' music video below: