Wells, whose future has been the subject of intense speculation during this month's transfer window, has signed a four-and-a-half-year deal with the Sky Bet Championship side.
The likes of Leeds, Middlesbrough, Burnley and some Premier League clubs have all been credited with an interest in Wells, but Huddersfield have won the race to land the Bermuda international.
Wells is regarded as one of the best young talents outside the top two leagues with the forward having scored 53 goals for Bradford since joining the club in the summer of 2011.
Bradford were reluctant to lose their 15-goal top scorer, but have decided to cash in on the player with his contract due to expire at the end of next season.
Huddersfield boss Mark Robins is a huge admirer of Wells and sees him as a key addition to his squad at the John Smith's Stadium, with the forward in line to make his debut against Millwall on Saturday.
Robins told the club's official website: "We have tracked the progress of Nahki for some time and we are delighted that we have secured his signature.
"At just 23 he has huge potential, which he has proven at Bradford in the last two seasons. He fits into our ethos of buying young, hungry players who have experience and that we can develop.
"His goal-scoring record over the last 18 months is hugely impressive and we believe that he is ready to make the step up to the Championship. He will excite our fans and has already shown them what he can do with his goal in the Capital One Cup. I believe he will offer our frontline something different and I can't wait to watch him in action for Huddersfield Town.
"For a young man he has already achieved a lot in his career having reached the Capital One Cup final and promotion with Bradford.
"His achievements and potential meant that he was coveted by a host of Premier League and Championship clubs and I am delighted that he has chosen to join us."