The 26-year-old was the top scorer in the Scottish Premiership last season, netting 23 league goals despite Ross County only finishing eighth in the final standings.
Boyce, who is a Northern Ireland international, has signed a three-year deal at the club which will keep him at the Pirelli Stadium until 2020.
"I'm absolutely buzzing to finally get it done. There's been a lot of speculation so now I'm just happy to be here," he told the club's official website.
"I kept in touch with Jackson after he came down here. He has done well and it has been a good platform for him to come and play his football. He's been brilliant the past season and I just hope to come in and do the same. I want to go to the next level and, no disrespect to Scotland, but the English Championship is a step up in quality and I wanted to come and test myself."
Manager Nigel Clough added: "He's a good player who can get goals. He was the top scorer in Scotland which, when you consider the incredible season Celtic had, that's some going in itself. He's another late developer and Ross County is proving a good breeding ground for players after him and Jackson Irvine.
"Liam has done very well there for a couple of seasons and he's a full Northern Ireland international. Some people say he's not easy on the eye at times but he's a good all-round player. He's not blessed with pace but holds the ball up well and gets in the box.
"If you think of all the chances we created last season then, hopefully, if we can do the same again he can get on the end of them. He's the right kind of character and he is desperate to come down and prove himself in England."
Burton's previous record signing was the arrival of Irvine, who also joined the club from Ross County for a £250,000 fee last summer.