The Shin Bet, whose announcement effectively ended a gag order on the arrests, said that the two used a car issued to Zubeidi by the Palestinian Authority during the attacks.
The two suspects were arrested in February. The weapons allegedly used during the attacks, including an M16 rifle, are now in the hands of the Israeli security forces.
Zubeidi, who led the Al-Aqsa Martyrs' Brigades, the Fatah military wing, in the Jenin area during the Palestinian uprising in the early 2000s, was pardoned by Israeli security forces as part of a deal signed with the Palestinian Authority in 2007.
Zubeidi and others were taken off the list of terrorists wanted by Israel and guaranteed their freedom as long as they refrained from violence or any terrorist activity.
The 43-year-old Zubeidi, a resident of the Jenin refugee camp, was subsequently given a senior position with the Palestinian Authority, in the Ministry of Prisoners' Affairs, often with his alleged accomplice, attorney Tarek Bargut, an Israeli citizen and resident of the West Bank city of Ramallah.
A Shin Beit source described the charges against Zubeidi and Bargut as very serious.
He added that intelligence and security forces investigated the attacks in their immediate aftermath, including actions taken inside Ramallah, which is the seat of the Palestinian Authority, and those investigative actions led to the suspects arrests while thwarting more attacks.