Mourinho, well known for playing mind games - particularly with Arsenal manager Arsene Wenger, fired a shot at his arch rival on Friday, claiming Fabregas had never been interested in leaving Barcelona for the Emirates Stadium.
Fabregas' contract with Barcelona had a clause allowing Arsenal first refusal if he left the Camp Nou.
"I spoke with him for 20 minutes," Mourinho said.
"I think he really wanted to come to us.
"As you know Arsenal had an option where they could interfere but I think he was not open to that. He was very much in our direction. It was an easy job for me."
The 27-year-old midfielder will now line up for Arsenal's London rivals Chelsea as one of three players signed by Mourinho from Spain's La Liga in this close-season.
Filipe's former Atletico team-mate, Diego Costa, is the other player to have swapped La Liga for the Premier League at Stamford Bridge.
"I have to say my club did a fantastic job and not just because of what we bought but a fantastic job because we did it almost in record time," Mourinho said.
"The market closes at August 31 and we close our market on July19. We finished our market today.
"The club did fantastic. We knew the targets, we knew the players. The club attacked them and their clubs at a very early stage. We got exactly what we need. The squad is a squad I like very much."
