The Bosman signing, who was Preston's player of the year last season, could start at right-back if ever-present Steven Reid is ruled out due to a hand injury.
"It will open the door for Billy," Hodgson told the WBA website.
"He is ready for the Premier League and we believe in him. Of our signings this year, I believe Dawson and Jones will go on to be very big players for the club.
"Long is another one. McAuley and Gera, who are older players, will also do well.
"I'm very happy with the squad We are stronger, I think, on paper than we have been.
"Right from the first moment we thought we'd done the right thing bringing Billy in - and he's improved.
"On each occasion he's done well and he's getting better and better.
"We believe in him strongly."