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"I'm the happy one," the 50-year-old Portuguese told a packed news conference at Chelsea's Stamford Bridge ground in west London.
"Time flies. It looks like it was a couple of days ago but it was nine years ago and since then lots of things have happened in my professional life.
"But I have the same nature. I'm the same person, I have the same heart. I have the same kind of emotions related to my passion for football and my job, but of course I am a different person...
"If I have to describe myself, I would describe myself as a very happy person because it's the first time I arrive at a club where I already love the club."
Mourinho led Chelsea to back-to-back titles during his first spell between 2004 and 2007 but left after a reported falling out with club owner Roman Abramovich.
But he maintained that those reports were false, instead saying that he left "by mutual agreement", albeit with a heavy heart.
Mourinho went on to manage at Inter Milan, where he won the 2010 Champions League, and latterly at Real Madrid before signing a four-year deal at Chelsea earlier this month.
He was only able to return because his relationship with Abramovich had not soured, he added.
"I think I'm back because we are in the best moments of our careers and ready to work together again. There are much better conditions at this time to succeed and have what we want, stability," Mourinho said.
Mourinho famously described himself as the "special one" at his first news conference for Chelsea nine years ago.
In his first three-year stint at Chelsea, he won two league titles, one FA Cup and two League Cups.
Asked if he could repeat or even better those achievements, he added: "If we work well, success will arrive."
