The chart topper – whose latest single Someone You Loved features Dr Who star and distant relative Peter Capaldi in its video – is bringing his show to the venue on Saturday July 20.
A limited number of tickets went on sale early to fans, but demand has been such that they have gone.
General sale starts tomorrow morning, with tickets going on sale at 9am via www.scarboroughopenairtheatre.com or in person from Scarborough Open Air Theatre Box Office (01723 818111) and the Discover Yorkshire Coast Tourism Bureau (01723 383636).