The prolific attacker admits he never imagined he would wear the famous Blaugrana shirt and is desperate to move on from this summer's biting incident.
The attacker joined Barcelona from Liverpool in a deal worth 88 million euro this summer, and he is delighted to have fulfilled a lifelong dream by making the move to Camp Nou.
Speaking at a news conference for the first time after his suspension from football was reduced, the 27-year-old said: "I want to thank the club and all of the directors for the confidence they have had in me, and of course the coach Luis Enrique and all of the people who have supported me.
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"I am looking forward to enjoying myself here and enjoying the group dynamic. I've been wanting to play for Barcelona for years and it's a dream come true to be here.
"I have been dreaming of playing for Barcelona for years. All the little boys want to achieve this. I didn't think it would ever happen, so I didn't think twice when the chance came up."
The Uruguay star then went on to voice his delight with his debut in the 6-0 win over Leon on Monday, though he claims he does not consider himself the club's star signing of the summer.
"It was very exciting to make my debut. I had never played at Camp Nou before, so it was very interesting to come out and see the fans. It was unbelievable. I never imagined something beautiful like this would happen," he said. "Am I the star signing? Stars are up in the sky. I am just here to do everything for the team. It motivates you to play alongside big names such as Lionel Messi and Neymar, but it's about all of the players.
"The coach has said some nice things to me, even though we didn't have an in-depth dialogue yet. He's focused on Elche for now. We will speak in more detail when my official debut gets closer."
Suarez also was questioned about the biting incident involving Italy's Giorgio Chiellini, and he stressed that he has spoken to professionals to ensure there will be no repeat of the incident.
"It's a personal matter which I would rather not discuss, but I have been speaking with professionals," he said. "My psychologist told me to get out and offer my apologies and I did that. I now want to move on and focus on football.
"Of course I was concerned after the Chiellini incident and not just about my transfer to Barcelona, but also about my reputation as a person. But that's in the past now."
Suarez could make his official Barcelona debut in the Clasico against Real Madrid on October 26, the day after his suspension comes to an end, and he has made it clear that he will be ready to face the Champions League holders.
"My debut against Madrid? It's still a long time. I don't think fitness will be an issue, but there's always the matter of adapting to the team," Suarez said. "But I don't think there will be a problem if I'm physically all right."