Mourinho was officially unveiled on Monday to start his second tenure at the club he won six pieces of silverware in a little over three season, including two Premier League titles.
And Carvalho, who believes Mourinho will bring the title back to Chelsea after a three-year absence, has backed the 50-year-old to hit the ground running after a difficult spell at the Santiago Bernabeu.
| MOURINHO: I AM THE HAPPY ONE
|10/1||Chelsea are 10/1 with Coral to win the Champions League next season
"He has the respect of everybody at Chelsea, the fans love him and the players know how he works. He is a great coach and gets results. Chelsea can improve their consistancy in the league and I think he will do that."
Carvalho - who recently signed for free-spending Monaco - says the Blues were still firmly in his heart after racking up over 200 appearances for the club, winning three Premier League titles and three FA Cups in the process.
He continued: "I still look out for the club, Mourinho knows I like the club and when we spoke in Madrid we would talk about it and he would tell me the results of the matches."