Despite Preston's relegation from the Championship last season, he netted an impressive six times from his 45 starts and finished the campaign as captain.
Sporting & technical director Dan Ashworth told the WBA website: "We're delighted to have signed Billy, who has just enjoyed an excellent season in difficult circumstances at Preston.
"He has consistently improved as a player as he has progressed up the leagues and we believe that trend will continue at this club in the Premier League.
"Billy is predominantly a right-back but he can also operate at left-back, centre-half and even as a holding midfielder. This versatility made him a very attractive option for us and his ability in the air for a full-back is also a major strength.
"He is a young, hungry player who is looking to improve which makes him a perfect fit for what we're trying to achieve as a football club."