The Ghana international, who played under the Portuguese during his first stint at Stamford Bridge and at Real Madrid, believes the Blues will have a very successful season
The Blues have not won the Premier League since 2010, and finished 14 points behind champions Manchester United last season.
But Essien is convinced the club can challenge for silverware in every competition they enter this season, and believes Mourinho can help Chelsea recapture the form that produced back-to-back titles in his first stint at Stamford Bridge.
"When I scored my last goal for Real Madrid on the last day of the season, I ran over to celebrate with him [Mourinho] and was expecting him to congratulate me when I hugged him," Essien told Sky Sports.
"Instead he leaned over and said: 'See you at pre-season training on July 8'. I found that so funny.
"We are now back together where we belong and where we had so many beautiful years together and I hope we can recreate those magical years.
"We are definitely going to give it a go this season. All the trophies are up for grabs and you can rest assured we will do all we can to bring as many as we can to the Bridge."
Essien has struggled with a host of injury problems in recent seasons, and his times at Chelsea looked to be over when he was loaned out last term, but the Ghanaian is fit against and ready to give everything for the club.
"I am ready to give my all to Chelsea," Essien added.
"I haven't lost any desire or motivation. I have been working hard in the last few weeks to be physically and mentally fit for the season and I feel good about my work so far."