On Monday, Belgium star Hazard was confirmed as the Blues' second summer signing almost a week after announcing he had decided to join them from Lille.
The 21-year-old admitted Chelsea's Champions League triumph convinced him they were his ideal destination and immediately set his sights on bettering that achievement.
The Blues also won the FA Cup but finished only sixth in the Premier League and Hazard told their official website: "Chelsea had a great season, even if we didn't do very well in the league.
"By anybody's standards, winning two cups is a great achievement, so it will be a big challenge to do better.
"We're equipped to do that, and all I can hope is that, while I'm here, we can win a lot of trophies. That's what I'm aiming for."
Hazard, who reportedly cost £32million, has followed in the footsteps of Lille team-mate Joe Cole in signing for Chelsea, with the former England international having done so eight years ago.
"I spoke to Joe Cole and what he said above all was that Chelsea was the right club for me," Hazard said after signing a reported five-year contract worth £170,000-per-week.
"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."
Hazard joins Marko Marin in signing for Chelsea in recent weeks, both individuals billionaire owner Roman Abramovich appears to believe can help deliver the exciting brand of football he craves.
Another is reportedly Porto forward Hulk, who is said to have agreed terms with the Blues on a four-year contract.
Brazil star Hulk, who has been valued at £38million, has certainly seemed to pave the way for a potential transfer by hinting the time could be right for him to leave Portugal.
The 25-year-old would fill the void left in Chelsea's squad by Champions League hero Didier Drogba, while Hazard would take the space of the out-of-contract Salomon Kalou.
The Blues also look certain to attempt to sign a new right-back after allowing Jose Bosingwa to leave, with Ajax star Gregory van der Wiel having long been linked with a move to Stamford Bridge.
Asked if he would be tempted by an offer from the European champions, the Holland international told Sky Sports News: "Yeah, of course. It would be a beautiful club."
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