The former England Under-20 international was Preston's player of the year last season despite their relegation to League One.
Hodgson said: "We're really pleased we've been able to secure his signature in the face of stiff competition from other clubs for his services.
"It is great that he has chosen our club as the place to further his career and we are looking forward to working with him.
"We have been monitoring Billy's progress for some time and, like the player himself, we believe this is the right moment for him to move up a level.
"He has been a very consistent performer in the Championship for a long period and this is his chance to show he can be as good a player in the Barclays Premier League."