The Blues star is expected to leave Stamford Bridge for Monaco in the next few days.
Fabregas has played 501 times in English football for Arsenal and Chelsea.
And David Luiz has revealed what the Spaniard said after what is believed to be his final appearance in a Chelsea shirt.
“He did a speech and then after that we all say thank you for him, and hug him,” he explained.
“I think it’s an emotional day not just for him, for everybody.
“One of the best players playing in England was him, everyone knows that.
“Sad for everybody when you lose this kind of player, this kind of person, but I think everybody has to stand up and clap the hands for him because he deserves it.
“It’s always difficult to lose players, especially like him, because like I say he’s a world-class player but also I understand it’s part of the process, and if it’s better for him and better for the club, we have to understand that.”
Luiz also opened up on how he will remember Fabregas as a ‘world-class’ talent.
He added: “I think he won everything with this club. My memories are always going to be with the world-class player, with the great technique, he’s a great guy.
“He has experience. He knows football, I think he had the opportunity to learn in many different changing rooms when he was so young, before, so he brings always a confidence, energy for the team, and then in the pitch he showed that it doesn’t matter the game, he’s always going to show his qualities.
“Sad. It’s really sad for us. We are wishing him all the best, because he deserves it.”
Fabregas will hope he can make a difference to Monaco.
Thierry Henry has been unable to change their fortunes and they sit second bottom in Ligue 1.
Chelsea return to action on Tuesday evening against Tottenham in the first leg of their Carabao Cup semi-final.