The Spain international moved to the Premier League champions in a £58m deal from La Liga giants Real Madrid last month.
Morata became the fourth summer signing at Stamford Bridge and bolstered Antonio Conte’s attacking line-up ahead of the 2017-18 season.
The 24-year-old will be tasked with helping to replace the goal void left by Diego Costa, who is expected to leave the west London club this summer.
Morata scored 15 times in 26 appearances in La Liga last season but struggled to secure a regular place in Zinedine Zidane’s los Blancos team.
Chelsea No10 Hazard, though, is looking forward to playing with the 24-year-old striker as Chelsea look to retain their Premier League crown.
“He’s won a lot, he is still young but he has a lot of experience. He can score every time,” Hazard told Chelsea’s website – as quoted by Metro.
“I hope to play with him soon.”
Morata won the Champions League title and the La Liga crown with Real Madrid last season following his £29m move back to The Bernabeu last summer.
The Spain international won two successive Serie A titles during his spell at Juventus but missed out on the chance to work with Conte in Turin.
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