The 24-year-old joins the newly-promoted Clarets from the Bundesliga outfit for their first season back in the Premier League after they won the Championship title last term.
The move sees Bruun Larsen reunited with manager Vincent Kompany, after spending the 2020-21 campaign on loan at Anderlecht under the Belgian.
The Denmark international becomes Burnley's ninth signing since winning promotion, joining Zeki Amdouni, James Trafford, Jordan Beyer, Dara O'Shea, Michael Obafemi, Luca Koleosho, Nathan Redmond and Lawrence Vigouroux through the door at Turf Moor.
"I'm really happy and excited to be here. I wanted to come to Burnley, the whole project really inspired me and as soon as I heard of the possibility, I knew it was what I wanted to do," he told the club website.
"It's a dream for me to be here and get the opportunity to play in the Premier League. I hope we can do great things this season and I'm really looking forward to it now."
Bruun Larsen joined Dortmund as a 16-year-old in 2015 and went on to make 41 appearances across all competitions for the senior team.
The winger has spent the last three-and-a-half seasons on the books at Hoffenheim, where he has scored five goals in 44 outings.
Under Kompany at Anderlecht in 2020-21, he scored twice in 19 appearances across all competitions.
The Dane, who has scored once in six caps for his country, could make his competitive debut for the club when they host champions Manchester City in the opening game of the new Premier League season on Friday, August 11.