The Czech Republic international made 80 appearances in total for the Rams after joining from Watford in the summer of 2016, scoring 27 goals in all competitions.
"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," Vydra told the official Burnley 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."
Vydra started his career with Czech clubs Vysocina Jihlava and Banik Ostrava, and has been capped 20 times by his country.