The 27-year-old scored 10 times in 43 Championship appearances for the Terriers during the 2016-17 campaign, but has dropped down the pecking order at the club following the summer arrivals of Steve Mounie and Laurent Depoitre.
"I have no doubt this is an ideal move for me," Wells told Burnley's official website. "I have played at every level besides the Premier League. I achieved that by getting promoted [with Huddersfield] and it wasn't something that was going to change. I have always wanted to play there.
"I've documented that way back, when I first broke into the game. Now the opportunity is here and I'm very thankful to the football club to give it to me. I feel I can go on and do great things.
"Burnley is becoming an established Premier League side. It's a group I'm sure I can come in and blend with really quickly and it's about trying to get out on that pitch as soon as possible and hit the ground running.
"The facilities are fantastic and it has everything you need to take my football to the next level. I'm here to grow. It's a step up for me and it's one that I'm relishing. I don't see why I can't learn of the strikers here and hopefully find a combination with the attacking options and play my part in helping move this club forward."
Wells is currently on the sidelines recovering from ankle surgery.