The Belgium international joined the Blues for a reported £13 million in 2011 but has struggled to establish himself in the first team, making eight Premier League appearances last season.
Lukaku will wear the No.20 shirt for the Baggies but will not feature in Friday's friendly against Nottingham Forest.
"I'm delighted to welcome Romelu to the club," Steve Clarke told the club's official website.
"He's a strong, powerful centre-forward who is young, enthusiastic and eager to learn. He was also desperate to come here.
"Romelu had a lot of Europe's top clubs chasing him when he joined Chelsea from Anderlecht for big money a year ago and also had several Premier League teams wanting to take him on loan this summer, so we've done well to get him.
"With the calibre of strikers Chelsea have got, he's found it difficult to break into the first team at Stamford Bridge.
"But he's had a season working at a top Premier League club and he now needs more minutes on the pitch.
"We're more than happy for Romelu to continue his development with us. I am sure he will be a big help to the squad over the course of the season."
The Antwerp-born forward rose to prominence with Anderlecht in the Jupiler League in Belgium, making his debut as a 16-year-old.
He scored a total of 31 league goals in his first two full senior seasons despite his young age, finishing as the division's top scorer during the 2009-10 campaign.