The 21-year-old former Everton trainee will compete for a place with Luke Steele at Barnsley, who were relegated from the Sky Bet Championship at the end of the season.
"I can't wait and get back to training and for the season to start," Davies told the Tykes' website.
"I started off at Everton when I was 14 and spent five or six years there before moving to Sheffield Wednesday. Hopefully this is the start of a new chapter for me at Barnsley.
"I've worked with some top goalkeepers in Tim Howard and Chris Kirkland who were very good with me.
"I'm not here to sit and watch, but I'm here to give Luke Steele a lot of competition over the season and play games."