Dunne is yet to make a first-team appearance for the Clarets after coming through the academy setup, but the 20-year-old spent last season representing Barrow and Accrington Stanley.
Burnley have handed Dunne a new two-year contract, but the player will look to continue his development in the Scottish Premiership with Hearts.
Dunne told the club's official website: "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.
"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."
The Edinburgh-based club currently sit at the top of the standings.