Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
Midfielder Essien spent last season on loan at the Bernabeu and scored in Mourinho's final match in charge, a 4-2 win over Osasuna, before being informed of his manager's intentions.
Two days later Mourinho's return to Stamford Bridge, following an absence of nearly six years, was confirmed.
"When I scored my last goal for Real Madrid on the last day of the season, I ran over to celebrate with him and was expecting him to congratulate me when I hugged him," Essien wrote in his blog on chelseafc.com.
"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."
Essien moved to Real on a season-long loan after falling down the midfield pecking order with the Blues and was happy to rekindle his special relationship with Mourinho.
Now the Ghana midfielder hopes to enjoy success with the Portuguese at Chelsea for a second time.
"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.
"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."