The Spain international was not thought to be part of Barcelona’s plans as new manager Luis Enrique rebuilds the squad after a rare season without any silverware.
A clause in the 27-year-old’s contract gave Arsenal first option to re-sign Fabregas, but Wenger informed the player’s agent he was not interested in any deal after signing Germany international Mesut Ozil last summer.
And after weighing up his options, Fabregas decided to return to the Premier League after talks with Chelsea boss Jose Mourinho.
Fabregas said: "There came a moment when I decided my time at Barcelona was over and I only tried to look for the best option for me.
"Arsenal were the first option due to a clause in the contract. We spoke with Wenger and he said that with Ozil they had this position well covered.
"From there, I had other very good offers and I looked for the best in the Premier League, which is where I wanted to go.
"I spoke with Jose Mourinho and he won me over, he convinced me, told me what I wanted to hear and from there everything was very quick."I hope that this new phase of my career goes phenomenally well."