The Czech Republic forward was the top scorer in the Championship last season with 21 goals and has signed a three-year contract at Turf Moor containing the option of a further 12 months.
Vydra's arrival continues a flurry of transfer activity for Burnley as Thursday's deadline approaches, with Joe Hart secured from Manchester City earlier on Tuesday, while club-record signing Ben Gibson joined Sean Dyche's squad from Middlesbrough over the weekend.
"I think five years ago I was like a kid in the Premier League. Now I feel I have more experience in English football, I speak better English and I have learned more in England, so I hope I'm a better player than five years ago," the 26-year-old told Burnley's official website.
"For the last four years I have been fighting to be in the Premier League.
"I haven't done it with the teams I was playing for and sometimes it has to be done with a transfer. Now I'm so happy."
I would like thanks all of you guys for your great support last two years. I will always have great memories, especially last ,, golden boot “ year! Wish you all the best and help the lads go to PL . — Matěj Vydra (@vydra_92) 7 August 2018
Vydra will compete for a place up front in Dyche's line-up with Chris Wood, Sam Vokes and Ashley Barnes, while further attacking reinforcements could be on the way if reports linking Jay Rodriguez with a Burnley homecoming from West Brom prove accurate.
"My ambition is to play in the best league in the world so thank you to the gaffer here and to Burnley for giving me a hand to play in the Premier League," Vydra added.
"Now it's [up to] me to show he chose the right person and hopefully I will be successful with mine and Burnley's targets."