The 21-year-old defender signed a four-year deal.
The England under-21 international spent last season on loan at Bristol City, he played 32 games in all competitions.
Speaking about the new signing, Bristol City Chief Executive Officer Mark Ashton said:
We saw first-hand last season just how talented Jay is and he quickly earned the respect of the City supporters.
His talents are clear for all to see and I am delighted we have been able to make Jay a permanent figure at this football club.
He has all the attributes we’ve been looking for and he will continue to flourish in the set-up and style of football which Lee Johnson and his staff have implemented.
Bristol City manager Lee Johnson added:
Jay proved to be such a great fit for us and is committed to helping City grow further. He is a young English player, with fantastic ability, and he will only become a better player.
With Lloyd Kelly’s move, it was a priority for us to secure an established left-sided player and, having fulfilled that role along with Lloyd last season, Jay was a player we were very keen to bring here permanently.
He is energetic, quick and has the ability to both defend and attack, so he is an exciting addition to the squad and I am delighted we can continue to work with him.”