The striker, who scored 27 goals in 80 appearances for the Rams, has signed a three-year deal with the Premier League outfit.
"I think five years ago I was like a kid in the Premier League," Vydra said.
"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," Vydra told the Clarets' 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 and now I'm so happy.
"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 and now it's about me to show he chose the right person and hopefully I will be successful with mine and Burnley's targets."