Wisdom, an England Under-21 international, spent much of last season on loan at Derby County in the Championship having come through the youth system at Anfield.
Despite making a handful of appearances for the Liverpool first team, he has struggled to cement a regular place at the club and will hope to establish himself at The Hawthorns during the coming campaign.
He becomes West Brom's sixth signing of the close-season, after Joleon Lescott, Chris Baird, Sebastien Pocognoli, Craig Gardner and Brown Ideye.
Head coach Alan Irvine told the club's official website Wisdom would make a fine addition to his squad for his debut season in charge.
"I'm delighted to welcome Andre to the club," he said.
"I've spoken to Brendan Rogers, who I've known for a very long time and who I trust implicitly. He said Andre would do a good job for us. That was reassuring.
"You want to find out about the person. You can see the player but you want to find out what they are like as a person. Brendan spoke very, very highly about him.
"He's a versatile lad. He's played as a right-back for Liverpool in the Premier League last season, he also played as a full-back for Derby.
"He grew up as a centre-back and played on the left side of central defence for Liverpool against Preston on Saturday."
‘I said yes to Manchester United, even though it was tough to understand everything that Sir Alex Ferguson was saying, but Borussia Dortmund said no’: Robert Lewandowski reveals failed Old Trafford move a decade ago
‘Every time Trent Alexander-Arnold has a bad game now, questions are going to be asked about his commitment – it baffles me that Liverpool have let his contract run down’ Former Anfield star bemused by lack of resolution over full-back’s future
