The 19-year-old joined Chelsea from Anderlecht for a reported £13million in August 2011 but struggled to break into the first team and was unable to score in just eight appearances for the Blues.
He has attracted the interest of a number of Premier League rivals this summer after it became clear that Chelsea would be prepared to loan him out to gain more experience.
The Belgian youngster’s agent revealed earlier in the week that a move somewhere was close, whilst ruling out Fulham as a possible destination, and the Baggies have now won the chase for his signature.
“I’m delighted to welcome Romelu to the club,” said boss Steve Clarke.
“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.”
Lukaku is looking forward to the challenge of playing for a team he admires for their playing style and hopes to make an impact.
He said: “I’m very excited. After last season, where I was able to adjust and prepare for this season, I can’t wait to start at West Brom.
“It’s very important because, like Chelsea, West Brom play in the Premier League, but it will also be a good learning school for me where I need to work hard with the players around me.
“I’ve heard a lot of positives about Steve Clarke here and it will be important for me to listen and learn from him. He plays good football.”