The 23-year-old Australia international, who left Albion at the end of last season by mutual consent, has agreed a three-year contract.
Town manager Chris Powell told the club’s official website: “A lot of hard work has gone into bringing Jason to the club, so it’s fantastic that he’s joined us ahead of the start of pre-season training on 1 July.
“Recruiting a top-quality left-back was a key priority in this transfer window and we believe we have achieved this in signing Jason.
“He possesses the attributes that we were looking for in a left-back; he is an athletic player who has attacking ability, but most importantly he is a good defender.
“As a left-back in my playing days, I believe the latter is the strongest quality required.”
Davidson is Powell’s second signing this week after he brought in midfielder Dean Whitehead from Middlesbrough.