The 20-year-old has joined the Jambos on loan for the 2018/19 season. He has also penned a new contract that keeps him at Turf Moor until 2020.
"The new contract gives me not only security, but a chance to be part of a club that is really progressing and has been on the up for the past few seasons," said Dunne.
"For me to remain part of that is a massive thing for me and my development.
"I will still be in contact with the coaches at Burnley and this time next year hopefully they will see me in a higher position than this summer.
"Hearts have been unfortunate with injuries, particularly at the back, and I feel lucky to have been able to get this deal to hopefully help plug the gap and play in some huge games.
"I know that Hearts have been off to a great start and they're going to look to continue that run, so I just want to be a part of that.
"It's a club with an amazing fan-base and seems similar in philosophy to Burnley, which should help me fit in really well."