The Uruguay striker had been in limbo since FIFA imposed a four-month ban from all football-related activity after his infamous bite on Italy's Giorgio Chiellini at the World Cup.
Suarez, who cannot feature for Barcelona in a competitive match until October 26, admitted he is also seeking professional help to avoid any further lengthy sanctions.
"The dream of playing for Barca comes from many years ago, as a kid. Everyone knows my relationship with family living here," he said.
"When I came to watch games here, I thought 'One day I will play here'. But it seemed something far away. There were offers from other clubs but when the Barca option came up I didn't think twice.
"My ban is what it is and we have to accept it. I have apologised and I've been talking to professionals in order to deal with it. I say to all the fans do not worry about that. I won't be doing that anymore.
"It's a difficult moment for me. I had the same situation last year at Liverpool (when he was banned for biting Branislav Ivanovic). I started to play on September 20 but I was able to train and help my team-mates off the pitch.
"I'm here to do important things at Barca. Everything that happens in the past, that needs to be forgotten. If I start thinking about everything I've gone through, I wouldn't be able to sleep."
After the Court of Arbitration for Sport eased some of the sanctions imposed by FIFA, allowing him to train with his new team-mates, Suarez came on for a late cameo in a friendly against Mexican side Leon on Monday.
"Playing at the Camp Nou yesterday was spectacular, very emotional. I still can't believe it. This is a dream come true," he added.
When asked if he felt any pressure over his £75m price tag, Suarez said: "Being a super star? The stars are in the sky. I'm here to help the team to try to win trophies."
Haha, The Fine? That will really hurt. Thats like me biting someone in my place of work and getting fined 78p. I would round it up to 80p because thats how much a packet of Quavers or a Topic are in the machine. The bans are heavy though, and rightly so.- hump3.