Vilanova, who replaced Pep Guardiola at Camp Nou last summer, has been absent from his post since late December when he was admitted to hospital for treatment on throat cancer.
The 44-year-old is scheduled to return to Barcelona at the end of the month, and when asked on a local radio station if Vilanova will still be in his role next term, Zubizarreta said: "Yes, absolutely.
"Tito will arrive at the end of March. I don't know if it will be March 25th, we have to be prudent with the date.
"After that, he will set the agenda. If he wants his first day to be in the morning, afternoon or evening, then fine. He decides.
"Tito is very well. But we know that these types of treatments wear you down.
"We're happy with how the process is going."