The 23-year-old has moved to The Hawthorns from Dutch club Heracles Almelo after passing a medical.
Davidson has made 10 appearances for Australia and featured in their three group games against the Netherlands, Spain and Chile at the World Cup last month.
His switch to the Baggies was held up while he resolved a contract dispute with Heracles Almelo as he believed he was a free agent but the club insisted he remained their player as they had triggered a one-year option.
Albion eventually paid an undisclosed fee in order to complete the deal.
West Brom head coach Alan Irvine told his club's official website: "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.
"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 becomes Irvine's seventh signing following Pocognoli, Craig Gardner, Joleon Lescott, Chris Baird, Brown Ideye and Andre Wisdom.
Very talented young player. I watched all of Australia's WC games and he was outstanding. Brom definitely has a future star of the PL on their hands.- pencil