The deadline-day switch sees Wells, 27, put pen to paper on a three-year contract at Turf Moor, as Sean Dyche's men add to the arrival of Chris Wood from Leeds United as they replace Andre Gray, who joined Watford.
"I have no doubt this is an ideal move for me," the striker, whose Huddersfield deal only had a year left to run, told Burnley's website.
"I have played at every level besides the Premier League. I achieved that by getting promoted 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."
Wells spent three and a half years with Huddersfield and played in 46 Championship matches - including the play-offs - last season, scoring 10 times as David Wagner's men won promotion.
Dyche added: "We welcome Nahki as another striking option and a player that is different to those we have.
"He holds a different skillset and therefore we feel can only enhance our attacking options in due course."
WELLS: “I have no doubt this is an ideal move for me. Now the opportunity is here and I feel I can go on and do great things.” pic.twitter.com/gN8HbndFKk— Burnley FC (@BurnleyOfficial) August 31, 2017
Wagner wished the striker well after a Huddersfield career that saw him score 49 goals in 153 games.
The Huddersfield boss said: "Nahki is a great character and has been a very important player for Huddersfield Town for a long time but now this move works for everyone.
"He is a very good player but at this moment in time we have a number of high quality players and options in our offensive line.
"Everyone here at Huddersfield Town would like to thank Nahki for what he has done for the club and wishes him all the best for the future."