The Belgium international described the returning Portuguese manager as “special”, while he also admitted he would like to add more goals to his game next season
The 50-year-old's appointment was officially confirmed on Monday as he returns to the west London club following spells with Inter and Real Madrid during a nearly six-year absence.
And though Hazard admits he may be "intimidated" by the two-time Champions League winning coach, the Belgian is delighted to get the opportunity to play under him.
"They already knew for a long time at Chelsea that he was going to sign and they all told me that it would be a good thing for me," Hazard told The Guardian.
"Jose Mourinho is someone special and it's a pleasure to have him as a coach. Maybe in the first training session I will be a bit intimidated - after all, it's Jose Mourinho.
"But he is also a man, with two arms and two legs and so, in the end, I will have a normal relationship with him, just as I have with my previous coaches."
Hazard enjoyed an impressive debut campaign in England following his arrival from Lille last summer, notching 23 assists and scoring 13 times in all competitions.
But despite that return and a nomination for the PFA Player of the Year, the 22-year-old is determined to add more goals to his game.
"This season I gave a lot of assists but next season I want to score more goals… I want to score 50 or 60 like [Lionel] Messi or [Cristiano] Ronaldo," Hazard continued.
"I lack that killer instinct. Messi and Ronaldo are born to score, it's in their nature but I still choose the nice dribble or the beautiful pass too often. I have to shoot more."
Chelsea have been linked with a number of players since Mourinho's arrival – including Marco van Ginkel and Daniele De Rossi – and Hazard is adamant he does not fear competition.
"Being linked to players is normal at big clubs, and certainly at Chelsea, where everyone knows the reputation of [the owner] Roman Abramovich," Hazard added.
"He buys a lot of players. At such a club you never have time to rest. You have to be 100 per cent all of the time. But even if Chelsea bought nobody, I would still have to fight for my position."