The Bermuda international made a name for himself in Bradford's run to last season's League Cup final, and has scored 14 goals in 19 League One games this term.
His fee surpasses the £1.2 million Huddersfield paid to Bristol Rovers in July 1996 for the services of Marcus Stewart.
Wells has signed a four-and-a-half-year deal and joins a potent forward line, which also includes the likes of James Vaughan and the in-form Martin Paterson.
The 23-year-old's career began with spells at the Dandy Town Hornets and Bermuda Hogges in his home country, before he moved to England and had an unproductive stint at Carlisle United.
His fortunes changed drastically after a move to Bradford, however, and he racked up 53 goals in 112 games for the Yorkshire club in a 30-month stay at Valley Parade.
Huddersfield boss Mark 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 goalscoring 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 is eligible to make his Huddersfield debut in Saturday's Championship clash with Millwall at the John Smith's Stadium after signing an emergency loan deal, which will be made permanent on Monday.
