The midfielders were teammates at the Gunners prior to the Spanish international's move to Barcelona in 2011.
The 30-year-old told Goal.com: "I had an amazing time with him at Arsenal and he stayed a very close friend of mine.
"I'm a bit disappointed that he'll be playing with Chelsea rather than us, but I respect his decision. That's football, and I'm very happy for him because I'm sure that if he's moving back it's because he wanted it.
"It will be very strange to play against him, and it won't be easy, we were laughing about it when I saw him a few days ago, but I'm happy because it will give me the opportunity to see him a bit more than when he was in Barcelona."
Fabregas scored 35 goals in 212 appearances for Arsenal prior to his departure.