The Catalan club's director of sport claims they have signed the Uruguay international from Liverpool, though they are unable to unveil him because of his ban for biting
Barca agreed a fee with the Premier League club last week but are unable to unveil their new signing due to the terms of his four-month ban from all "football-related activity" for biting Italy's Giorgio Chiellini while on World Cup duty with Uruguay.
Suarez will be unable to train with his team-mates until the end of his suspension, unless an appeal with the Court of Arbitration for Sport is successful, but Zubizarreta is confident the 27-year-old will be a huge hit at Camp Nou.
"He is 100% a member of the club," he told reporters at a press conference. "And we accept people here, imperfections and all.
"I am sure Luis Suarez will be someone positive for us in the future. Luis Suarez is an important player for this club but the club is more than its players."
One of Suarez's new Barca team-mates, Lionel Messi, had occasionally vomited during matches in the past 12 months, causing some to question his health, but Zubizarreta is not overly worried about this issue when it comes to the World Cup Golden Ball winner.
"We are concerned about all health issues to do with Messi. But tests have been taken and we know what this diagnosis is. It's not a concern. Hopefully he will be at his best in order to compete after the summer," he added.