The 28-year-old has penned a three-and-a-half year deal at the Tynecastle club, with Hearts having already agreed an undisclosed transfer fee with the English side.
Boyce scored 14 times for Burton this season and was in the final six months of his contract.
The Northern Ireland internationalist is well-known to Scottish football fans, having spent a productive three years in the Premiership at Ross County. He scored 48 times in the league, including 23 during the 2016/17 campaign which saw him become the Scottish Premiership top scorer. He was also part of the side that defeated Hibs in the 2015/16 League Cup Final.
Boyce could line-up for his new side on Sunday against Steven Gerrard's Rangers, subject to international clearance.
The striker becomes Daniel Stendel's third signing as Hearts manager, following the capture of Kosovan winger Donis Avdijaj and Toby Sibbock on loan from Barnsley.