The successor to Power's Fleadh festival takes place on June 18 in Finsbury Park and is expected to feature a number of Irish acts.
Power said: "The inaugural London Feis will be a fantastic edition to the capital's summer calendar and announcing Bob Dylan for an exclusive UK performance means that the first year will be one to remember.
"I've worked with Bob many times before and am delighted to have him back once again."
Further acts will be announced over three stages at the event. Tickets are priced at £70 and are available now.
Dylan last year headlined Power's Hop Farm Festival in Kent.