Huddersfield accepted a bid from Wolves on Thursday and Coady has agreed a three-year deal after passing his medical.
“We’re sad to see Conor leave, but this transfer represents outstanding value for Huddersfield Town and we believe it is the right move for the club on balance,” Huddersfield boss Chris Powell told his club’s website.
“Conor also expressed his desire to pursue this opportunity, but we made it clear that the club would only sell him if the terms were right for Huddersfield Town; there was no cheap deal to be had.
“Once the transfer deal was acceptable to the club, the move suited all three parties.
“Conor is a great young footballer and a fantastic individual, so I’m sure I speak for everyone connected with Huddersfield Town when I wish him the best of luck at his new club.
“Our overall plan will not change because of this move.
“Even before Conor’s departure, we were already working hard behind the scenes to recruit the right players in key positions ahead of the start of the 2015/16 Sky Bet Championship season.”
Coady was one year into a three-year contract at Huddersfield after joining from Liverpool in the summer of 2014.
He made 45 starts and three substitute appearances for Town last season and was voted the club’s players’ young player of the year.