The Anderlecht teenager's move to Stamford Bridge was confirmed on Chelsea's website after the two clubs agreed a fee for the 18-year-old, reportedly between £15-20 million.
"Amazing. It's a dream come true," Lukaku said on www.chelseafc.com.
"I dreamed to play here since I was 10 years old, thinking about shaking hands with all those players like John Terry and Frank Lampard and Didier Drogba.
"It's amazing to arrive here in a big club with big ambition. It was just what I was searching for."
Lukaku passed a medical at Chelsea last week and will be available for the club's Premier League meeting with West Bromwich Albion on Saturday.
Source: AFP
Source: AFP