The Spain international put pen to paper on a five-year deal at Stamford Bridge last week after spending three seasons with his boyhood club.
Fabregas left Barca for Arsenal at the age of 16, but returned home to Camp Nou in a big-money transfer in 2011.
Despite a return of 42 goals and 45 assists in his three campaigns in Catalunya, Fabregas struggled to establish himself ahead of the likes of Xavi and Andres Iniesta in Barca's first-team and often attracted criticism from some sections of the club's support.
Barca released a statement following the 27-year-old's sale to Chelsea claiming there had been a "downward trend" in his performance level in each of his seasons there.
However, Fabregas - who joined Chelsea after Arsenal rejected the chance to re-sign him - has insisted he was not forced out of the club and claims that he requested to move on.
"There were many, many factors. My numbers weren't bad, but it's true that in big games I didn't manage to find those goals or assists," he told Cope.
"But I leave satisfied. I have played with my friends and experienced incredible moments in the Nou Camp and outside.
"For me it was a great period, but it's over and I wanted to find something new. I left, I asked to leave."
Fabregas, who is currently away with his country's FIFA World Cup squad, went on to say he is relishing the chance to return to the Premier League.
"I know I'm going to be happy," he added.
"It's important that everything goes well on the pitch but I lived in London for eight years, I have a house there and my friends.
"It's only an hour-and-a-half from Barcelona, but I'm going to a new club and I'm sure it's going to go well."
