Arsenal had first option on their former player when he decided to leave Barcelona at the end of last season but he moved to Chelsea in a deal reportedly worth 33 million euros (£26.3 million) with a further 3 million euros (£2.4 million) linked to performances.
"We talked with Wenger but he said that he would find it difficult to make a place for me on the pitch as Ozil had my position covered," Fabregas told a news conference at Spain's World Cup base.
"There were some very good options and I chose between the best two or three," added the 27-year-old.
"I spoke with (Chelsea manager) Jose Mourinho and he said what I wanted to hear and things went very quickly from there.
"This is not the right moment to talk about this, though, as we need to be focused on the national team and the World Cup."
Fabregas was a second-half substitute for Spain as they crashed to a 5-1 defeat against the Netherlands in their opening game in World Cup Group B.
He said he and his teams mates were seeking inspiration from the last World Cup four years ago in South Africa when Spain went on to beat Chile in the group stage having lost their opener 1-0 against Switzerland.
"We need to think about what we have achieved over the past six years," said Fabregas, referring to Spain's European Championship triumphs in 2008 and 2012.
"You can't live in the past but there are positive things that can be taken from four years ago when we also played Chile and we won 2-1.
"It was a different situation as we didn't need as many goals and Chile were also qualified so they didn't need to fight but there are similarities.
"We will play our usual football style of keeping possession but we need to be more dynamic with the passing.
"There are different ways to play. We are known for our passing game and this is the moment to attack and be brave. We need to control the game and score a lot of goals."
- Sports & Recreation