The Baggies won the race for the 19-year-old Belgium star, who had been linked with a number of clubs, including Fulham.
Lukaku, who joined Chelsea for £18million last summer, will work under former Blues assistant manager Steve Clarke.
Boyhood Chelsea fan Lukaku struggled to break into the first-team squad at Stamford Bridge last season and was prevented from being loaned out under FIFA rules, having already played for Anderlecht.
However, those barriers were lifted this summer, much to Lukaku's delight, and he told Chelsea TV: "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."
Clarke, who was appointed to his first managerial post this summer, told his club's official website, www.wba.co.uk: "I'm delighted to welcome Romelu to the club. 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."