The 19-year-old joined was snapped up by QPR in 2012 when they signed him from South Melbourne.
But he will be moving to the Britannia Stadium from July 1, after agreeing terms with the Premier League outfit.
Skapetis will work with Glyn Hodges at Stoke, a man who was the main reason behind his switch to Loftus Road.
Now Sky Sports understands that Stoke will pay QPR an undisclosed fee for the teenager, who has agreed an initial two-year deal.
Skapetis commented on the move via his Twitter account and said: "This is a big opportunity for me to develop my game at a Premier League club.
"I think playing there can take me to another level hopefully and give me my best chance of success," he said.
"In saying that, I really enjoyed my time at QPR and appreciate the opportunity they gave me in chasing my dream of playing football in the UK and I wish them well in the play-offs.
"I feel it's time to move on. There's a chance for me and I want to take it. My ultimate goal is to break into the first team and hopefully this move will give me the perfect platform for that."