The German goalkeeper has been charged with the task of replacing Victor Valdes at Camp Nou after the long-serving Spaniard opted to seek pastures new.
Ter Stegen arrives at the club with an excellent reputation due to his exploits with Borussia Monchengladbach and at youth-team level for Germany.
Barca legend Zubizarreta has revealed that the 22-year-old has long since been on the Liga club's radar and is in no doubt that he can be a success.
He said: "It's a very difficult but exciting task. It's one of the great challenges but we think (Ter Stegen is) capable of dealing with that and doing well.
"He is very fast, agile and he's very decisive. He's also very good in the air and one-on-ones. There is still room for improvement but we've all got time to improve.
"He's very young but has a few seasons of experience in the Bundesliga playing for one of the bigger clubs in that league.
"(The transfer is) one of those that has taken some time but Marc has always shown loyalty to us because he also had commitments to Borussia.
"We've been after him for two or three years."
