The 38-year-old was released by Stoke to join the Clarets on a short-term deal until the end of the season, in a move that also saw Wales international forward Sam Vokes move in the opposite direction.
Crouch, whose previous clubs include Tottenham, Liverpool and Aston Villa, will be hoping to add to the 108 goals he has scored in the top flight throughout his career.
Now back in the top flight, Crouch says he is delighted to back in the Premier League and is excited to work under Clarets manager Sean Dyche for the remainder of the campaign.
He told reporters: "I'm pinching myself. I'm absolutely buzzing. I know Phil Bardsley, Joe Hart and Jon Walters and they only had good things to say about Burnley.
"Sean Dyche is a manager I have always admired. The move came out of the blue and it turned out to be a whirlwind day.
"I never thought I'd have the opportunity to play in the Premier League again, so to be given this chance is not something I am going to take lightly.
"I know Burnley are a proper club but I was blown away when I walked into the training ground and saw the quality of the facilities."