The Spain international joined for the Liga giants in a deal worth €36 million earlier in the summer, and played a part in all three goals in Monday's 3-0 win over Burnley.
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"When the players are your first choice it is very difficult to make a mistake," he told reporters. "Fabregas was our first choice for that position. I know clearly what the player is because we were so long in the same league.
"He moved to Spain also, so for the last 10 years we have been in the same league for six or seven. I know exactly what he will bring.
"For Barca he was the fake nine, the number ten and winger but I know and he knows what is his best position so he is giving exactly what we need. Quick thinking in midfield. He brings people in the same direction. I am really happy."
Chelsea overcame a shock Burnley lead to run out comfortable winners at Turf Moor and Mourinho praised midfielder duo Fabregas and Nemanja Matic for their assured displays.
"The team played very well but I agree with Cesc being man of the match because he and [Nemanja] Matic controlled the game and dictated the intensity of it," said the Chelsea manager.
"They decided how to control the pace. They were both good brains in this team and I am happy with that because last season we could not control the game as we controlled [it] today."