The teenager performed well during a week-long trial at Ulster earlier this year and will now join up with Kiss' men during their pre-season efforts in July and August.
Stapley, who plays at inside centre, only made his senior debut for the Exiles in January, aged 17, but scored a hat-trick for his side on Friday as they won the UAE Premiership and West Asia Championship double.
"It's very exciting, a chance for me to really go and prove myself as a player," said Stapley.
"It's a chance to show my game somewhere else and really push myself and my game to the best it can possibly be.
"I was there for a week in February and had tips from the coaches what to work on. It's good I've been invited back so I must have done something right.
"I'm aiming high, and the highest I can aim for is to be a professional. I will work as hard as I can to make that happen."
Stapley was recommended to the Guinness PRO12 side by the Exiles' director of rugby Jacques Benade, who spent time coaching in the province.
The back first represented Exiles as a six-year-old and, having come through the ranks at the Emirate club, praised the standard of coaching he has received.
"Jacques and the coaches have put a lot of trust in me," he added.
"Being 17, I had no idea I would have played as big a part or as many games as I have, but it's been great to do that.
"The level of coaching out here is excellent. To get people out here up to the required standard needed to go back to the UK, I owe a lot to them for where I am now, and I definitely won't forget that when I'm in Ireland."
To buy tickets for the Guinness PRO12 Grand Final click here. Also follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the Guinness PRO12.
Guinness PRO12 Ulster News
63x46.png){kind=logo}