The 18-year-old, who made his first-team debut against Derby in April, was already under contract until the end of the 2014-15 season but has now extended that deal by a further year.
Dawson made his Wales U21 debut earlier this season and moved up to the Leeds U21 set-up before getting his first call into Neil Warnock's side in what turned out to be the manager's final game in charge.
"I'm really pleased with how my season has gone and this is a reward at the end of it," Dawson told the club's official website.
"At the start, I was hoping to maybe get a one-year 'pro' by Christmas and then kick-on next season, but it's obviously gone a lot better than expected and I've got three years now.
"This will give me a lot more opportunities and I have more time to work things and improve.
"As a first year scholar I didn't get an opportunity all season, but this year I started in the 18s and I have become a better player by playing more games and I hope to carry that on next season as well.
"I moved up to the U21s and did well there, and I got my chance in the first team. Hopefully I can do well there next season. After my first year when I didn't expect to get anything at all, it's a great feeling.
"It was nervy at first, but once you're on the pitch it's okay. I'd never played at the level before, but you get used to it once you've done it. I try and stay level headed. I know what I need to do to become the player I want to be, so things don't faze me too much.
"The Academy has been really important. I've had a lot of encouragement from all the staff. It helps when you talk to them.
"I've spoken with the new manager (Brian McDermott) a couple of times and he seems like a really good guy. The style of football he plays suits me so I can't wait for it to start.
"I had a shoulder operation a few weeks ago which has gone well so I'm looking forward to pre-season now. If I can play a part in pre-season hopefully I can impress and see where it goes."