The carrier, set up by former WOW Air executives, will begin UK flights on 24 June.
It will operate to Stansted four times a week; on Monday, Thursday, Friday and Sunday, with one-way fares from £30. Flights will depart Stansted at 16.10.
The airline plans to extend the London flight to a daily service and to serve six other European destinations.
PLAY has scaled down plans for an initial fleet of six aircraft and now says it will have three Airbus A321neo aircraft, seating 192 and leased from AerCap. The remaining two will be delivered in July.
PLAY chief executive Birgir Jonsson said: “It’s brilliant to be able to open up Iceland to UK travellers and offer competitive fares now that international travel has resumed.
“While the UK market knows Iceland well, the destination has changed a little recently with the minor volcanic eruptions in the Reykjanes peninsula. Certainly a must-experience for UK travellers."
