The 21-year-old Lille playmaker, who had long been linked with a move to the Barclays Premier League, revealed he had chosen the newly-crowned European champions on his official Twitter account.
He wrote: "I'm signing for the champion's league winner."
Hazard earlier continued to keep fans of several clubs in suspense by posting he had "made up his mind" who he was going to join but declined to name the team in question.
There has been no official confirmation from either Chelsea or Lille that a deal had been reached over the signing of Hazard, who has been rated at £32million.
But reports in France suggest the Belgium star has agreed a five-year contract worth as much as £100,000 a week after tax.