The former Gunners captain rejoined Barcelona in 2011 but was never able to nail down a key role in the Blaugrana's first team and signed a contract with the Blues on Thursday.
"Arsenal was my first option for the contract clause [but] we talked with Wenger and my position was filled in his team," he said. "I had very good offers from other teams. I wanted to come back to Premier League, obviously, then I talked with Jose Mourinho and he said what I wanted to hear, he convinced me and nothing else. I'm very happy with this."
Fabregas came on as a substitute as Spain was beaten 5-1 in the first game of its World Cup defense against the Netherlands on Friday and is determined to improve in order to get out of the group.
"We are a national team and we know how we need to play," the midfielder said. "We can win in different ways. I'm not saying we should change the players but we have to be stronger in attack.
"This team can do it; I don't see why we couldn't have a great match against Chile and teach them a footballing lesson."