Fabregas signed for Chelsea after three years at Barcelona, despite a rumoured clause which gave the first option to Arsenal, where he played from 2003 to 2011, making 303 appearances and scoring 57 goals under Gunners boss Arsene Wenger.
The 27-year-old Spain playmaker has thrived on his Barclays Premier League return and next plays against Arsenal in Sunday's contest between the only remaining unbeaten teams in the league.
"I think he loves Chelsea already," Blues boss Mourinho said.
"He's so happy: the way he plays, the way he's a member of the squad, the way he lives in this little blue village.
"It is like he's (been) here for a long time
If you ask him now if he regrets the move, I'm sure he'd say no.
"If you ask him if he'd choose a different option, he'd say no.
"And if you ask him where he thinks he'll be in five years' time, he will say Chelsea.
"He is Chelsea
He is completely committed to Chelsea
And he likes Chelsea very, very much.
"One thing is that and another thing is to forget the past
I'm happy he doesn't forget the past."
Mourinho is adamant Fabregas remembers fondly the club he joined aged 16.
The Portuguese added: "I wouldn't be happy if he came here saying he didn't care about Arsenal.
"Many times, when (players) say that, it's not true
If it's true, it's also not good.
"He'll never lose his respect and his connection with a club where he arrived as a kid and left as a top player.
"He doesn't forget Arsenal, he doesn't forget the time he spent there, he doesn't forget the contribution Arsenal made in his fantastic career, and that deserves a place in his memory and his heart
For me, the approach is correct.
"The fact he's giving everything to Chelsea with such professionalism and enthusiasm is exactly what we want of him."
During his first spell at Chelsea and his time at Real Madrid, Mourinho never imagined Fabregas would come under his charge.
"I was at Chelsea, he was at Arsenal - a rival," Mourinho said
"I was at Real, he was at Barcelona - a rival
"It never looked possible that he would become my player
I never thought about it."
When the possibility arose, Mourinho moved swiftly for a player with supreme talents.
He promised Fabregas he would be the central figure in the team and not one on the periphery, like he was at times in Barcelona, where he played on the wings and as a 'false nine' forward.
"I wanted him because I know the player he is," Mourinho added.
"And I know he was good for the philosophy we wanted for the team.
"I knew that he's one of not many players who can play as a number eight or a number 10, so gives me possibilities to play him in both positions and build a midfield knowing that.
"This, plus the fact that he was made in England and played for so many years in English football
That's a plus.
"He doesn't need that adaptation
He comes back 'home'
We knew he was the perfect for us
We tried hard, and we got (him)."
Mourinho is not concerned whether Fabregas celebrates scoring against the Gunners, pointing to his own inner feeling of happiness when his Inter Milan side beat Chelsea in the Champions League in 2010.
"He should score, celebrate or not - I don't care," Mourinho said.
"When my team scored against Chelsea and my team did three times, two in Milan and one at Stamford Bridge, I didn't celebrate
I was happy, you can't imagine how happy I was.
"Not celebrating is nice
Show some respect."
Source : PA