The 24-year-old formally signed for the Catalan club earlier today in a deal reportedly worth £35m.
The Spanish midfielder had refused to discuss his future publicly in the weeks leading up to his Barca return, but has vowed to explain his reasons for departing to the Gunners' fans soon.
"I have time to talk about it and I'm sure I'll do an interview especially for them," Fabregas told a press conference at the Nou Camp.
"I'm sorry I couldn't say anything in the last two and a half months, Arsenal wouldn't allow me to talk to anyone. Even if I wanted to I couldn't.
"I'm disappointed and upset about it because I have had a great relationship with the fans over the years. It took time to build this and I'm disappointed I could lose some of them.
"All I have are words of gratitude. I'll never forget what they have done for me. I gave absolutely everything to the club and I think they know that."
Fabregas could make his Barca debut in the second leg of the Spanish Super Cup on Wednesday evening. The first leg ended 2-2 in the Bernabau yesterday evening.