The England international has fallen way down the pecking order at Anfield and had been strongly linked with a move away from the Reds during the current transfer window.
And, the Baggies have since struck a deal with the Merseyside giants to take the striker on board for the remainder of the 2017/18 campaign.
"This felt like the right fit," Sturridge told the club's official website.
"I've got friends here I've played with before, the manager spoke very well, the challenge with the team and the style of play. I just felt this was the right fit for me."