The 21-year-old spent last season on loan at Championship side Derby County, where he made 34 appearances.
Wisdom will now fly out to meet his new teammates at the club's pre-season training camp in the United States.
"I'm delighted to welcome Andre to the club," West Brom head coach Alan Irvine told the club's official website. "I've spoken to Brendan Rodgers, 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."
Wisdom will wear the number two shirt at The Hawthorns.