The 28-year-old was desperate to gain more playing time in order to stay in contention for England's World Cup squad.
“This felt like the right fit," said Sturridge on his move.
“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."
Sturridge, who has also played at Chelsea and Manchester City, was born in Birmingham. It is believed his ties to the city caused him to choose the Baggies over Newcastle United, where he was due to undertake a medical on Tuesday.