The Catalan club announced last Friday that Suarez will sign a five-year contract at Camp Nou after an undisclosed fee was agreed with Liverpool.
Barca have yet to formally announce the transfer, but Zubizarreta revealed on Wednesday that the controversial Uruguay star has finalised his move to Spain.
"He is now a Barca player in all respects," Zubizarreta said.
Suarez is set to miss much of the first half of the season after being banned from all football-related activity for four months following his bite on Giorgio Chiellini during his country's FIFA World Cup clash with Italy last month.
The 27-year-old also received a nine-match suspension from competitive international matches, and has seen an appeal against that sanction rejected by FIFA.
Suarez's lawyer Alejandro Balbi has confirmed he will take his client's case to the Court of Arbitration for Sport, with Barca president Josep Maria Bartomeu expressing his confidence that the player's ban will be reduced.
However, Zubizarretta was coy on that issue on Wednesday.
"Our lawyers tell us that we should be very, very prudent with what we say," he explained.
"We're speaking to our lawyers to find out the best way of defending his rights. But there is not much I can say in that respect."
