It was announced on Thursday that the Spain international had put pen to paper on a five-year deal at Stamford Bridge.
The move brings to an end his three-year stint at Camp Nou, whom he joined from Arsenal in 2011.
In a statement released on his official Facebook page, Fabregas confirmed that Arsenal had the option to re-sign him from the Catalan giants, but chose not to trigger that clause.
Instead Fabregas signed a long-term contract at Chelsea, one of Arsenal's direct rivals in domestic and European football.
"Yes, everyone knows that Arsenal had the first option to sign me," he said.
"They decided not to take this option and therefore it wasn't meant to be. I wish them well in the future."
Fabregas, currently with the Spain squad in Brazil for the FIFA World Cup, was delighted to have finalised the move before the defence of their crown, starting with Friday's Group B opener against the Netherlands.
"It was extremely important to me that this transfer was completed before the World Cup so that my mind will only be focused on hopefully helping my country try to retain the trophy," he added.
