Guler told a news conference the attacks were carried out by a cell linked to the al-Qaida terror group, and that it has been "put out of action and other possible attacks have been prevented," the BBC reported.
Last month, attacks on two synagogues, a bank and the British consulate in Istanbul killed 62 people.
The governor said 35 people had been charged so far in connection with the attacks.
"We can comfortably say that we have broken up the organization's Istanbul activities," Guler said.
He gave no further details of the investigation which had led to the arrests.
Earlier Friday, Turkey's Anatolia news agency reported that police investigating the bombings had found more than 1,000 pounds of explosives during searches in Istanbul.