The Socceroos left back has joined the Baggies on a two-year deal, having impressed for his country in Brazil at this summer's World Cup.
The 23-year-old left back, who featured for Australia at the World Cup earlier this summer, has signed a two-year contract with Alan Irvine's side.
"I'm delighted we've been able to complete a deal for Jason. He had a fantastic World Cup when he performed very well against three top teams," Irvine told the club's official website. "Jason is a good defender who has lots of energy, gets forward well and will give us competition for places at left back with Sebastien Pocognoli.
"Due to contractual issues with his former club, there's been a delay in Jason coming. This means he hasn't trained properly since the World Cup so he's going to need a little bit of time to catch up before we can expect him to perform at the levels he's capable of.
"I spoke to Tim Cahill about Jason and he recommended him very, very highly both as a player and character. Tim sees him as a young player who will do extremely well in England and develop even further."
Davidson made over 50 appearances for Heracles and has earned 11 caps for Australia.