The 24-year-old has penned a three-year deal with Huddersfield after impressing on loan last season, scoring 14 goals in 37 appearances in all competitions.
The former Everton forward signed for Norwich in June 2011 but made just six appearances for the club.
|16/1||Huddersfield are 16/1 with Coral to earn promotion next season
"James' arrival is a significant signing for the club and one that I know our supporters will be very pleased with after his excellent debut season in a Huddersfield Town shirt," Robins told the club's official website.
"Equally, I'm delighted that we have secured his services. The exciting thing is I believe there is even more to come from James.
"He is only 24 and although he already has excellent qualities in terms of strength, pace, work rate and much more, I believe he will have learned from the games he played last season and we will benefit from his knowledge and understanding of the style of football we want to play here."
Robins revealed that it took protracted negotiations with the Premier League club to sign Vaughan, but that the player himself jumped at the opportunity to return to The John Smith's Stadium.
"The club has been very patient to get the right financial deal in its negotiations with Norwich City and I believe we have secured that, but negotiations with James took almost no time at all – that was agreed some weeks ago after Norwich gave us permission to speak to the player," he said.
"He has shown such a huge desire to come to Huddersfield Town and turned down other, potentially more lucrative, financial offers."