Lukaku has agreed a season-long loan deal with West Brom.
"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."