The club's sporting director has dismissed concerns over the player's age after the 30-year-old was presented to the media at Camp Nou
The sporting director sanctioned a €20 million deal for the 30-year-old, who has signed a four-year deal at Camp Nou, with the option of an additional year.
The decision to offer a contract of that length is unusual for a player in his 30s, but Zubizarreta is convinced Barcelona's latest capture has plenty still to give.
"Mathieu is an excellent football player, that's what I think, and he will help us with our operation ahead," he told the media at the Frenchman's official presentation on Thursday.
"I will not get into numbers, for me that isn't important. It is said that when a player is 30-years-old he is finished and then later we see that he is not. He's in excellent physical condition."
The retirement of Carles Puyol and the club's struggles at the back in his absence last season meant defensive reinforcements were at the top of new coach Luis Enrique's wish-list this summer and Zubizarreta is glad to have delivered.
"Last season we made the decision not to sign any defenders from a technical point of view," he added.
"We made that decision together with the management. This year we wanted a player in the centre position who could help us improve. We're delighted to have fulfilled that desire."
The 52-year-old also refused to give guarantees over the futures of Alex Song and Ibrahim Afellay, who both appear surplus to requirements at Camp Nou.
"In the case of Song and Afellay, we are working on it. Alex has trained today, we will see what is going on, not just signings, but outgoings as well."