Hazard announced last week on his Twitter feed that he was on the way to Chelsea and he has now completed his transfer to the European champions and FA Cup holders after passing a medical.
The fee is undisclosed but according to media reports it is around £32 million.
"I spoke to Joe Cole and what he said above all was that Chelsea was the right club for me," Hazard said.
"As somebody who loves the club himself, he said he could really see me in the shirt, so when I see him next I'll tell him he was right," he added of Liverpool player Cole who spent last season on loan at French team Lille.
The versatile 21-year-old Hazard, who has been with Lille since 2005, will join up with Chelsea's squad for pre-season training next month.
A target for many of Europe's top clubs, Hazard said he was delighted to join the Londoners who next season will attempt to improve on their disappointing sixth-place finish in the 2011-12 Premier League.
"This is a wonderful club and I can't wait to get started and for the season to start so I can meet my new team mates, the supporters and all the people who are involved," he said.
Hazard, named best Ligue 1 player in the past two seasons, led Lille to the French title in 2011 and scored 20 goals in the last campaign including a hat-trick in the final game of the season to secure a third-place finish for the club.
He will join fellow Belgians Thibaut Courtois, Romelu Lukaku and Kevin De Bruyne at 2009-10 Premier League winners Chelsea.
"It's a dream come true for me," said Hazard. "I want to play as many games as possible, score as many goals as possible and win a place in the hearts of the supporters.
"It's true that initially there were a number of clubs in for me but when Chelsea won the Champions League I thought, 'why not?'," added Hazard.
"Ultimately for a player it's all about winning things. I want to win as many trophies as possible which is another reason why I came here as Chelsea have been winning things for a long time now."
Hazard will not feature in this month's European Championship in Ukraine and Poland because Belgium failed to qualify.