The 20-year-old defender, who became the Clarets' first signing of the summer, has agreed a four-year-deal – with the option of a further 12 months – at Turf Moor.
After progressing through the ranks with the Potters, the centre back went on to make 39 appearances for the club in the Championship, scoring twice.
“Everything about it is top drawer. It’s massive. It’s what I want to do,” said Collins, who became City's youngest captain when he led the side at the start of the 2019/20 season.
“I want to play in the Premier League. It’s going to be a jump but I think I can be ready for it.
“Every season they go into it, Burnley look dangerous. They can always hurt teams and it’s a really attractive team to come and play for.
“I want a challenge. That’s why I play football – to challenge myself and I can’t wait to get going.
“I want to play big games, I want to play against these players – I really can’t wait.
“Looking at Burnley, looking at what they’ve done in the last few seasons and what they want for the future; everything played a part.
“I think they do have big expectations at this club and I want to be part of it.”
Dublin-born Collins – a Republic of Ireland U21 international – joins the Clarets with Sean Dyche’s side preparing for a sixth successive season in the Premier League.
The Irishman is the latest in a long line of astute defensive acquisitions to have played under Dyche and he's looking forward to teaming up with the likes of captain Ben Mee, James Tarkowski and Kevin Long.
“Even watching them last season, they are really good, the way they talk to each other and the way they play,” Colins told Clarets+.
“I think they have really big roles in this team and is something to look up to.
“The gaffer here has improved many players before, which is another part of why I came to this club.
“I think I’m ready but I just want to improve myself. I want to get better and help this team. I can’t wait to get going for pre-season.”