Special forces police and members of the Israel Security Agency, or Shin Bet, tracked the suspect to a building in the northern Israeli town of Ar'ara, police spokesman Micky Rosenfeld said.
He emerged from the building Friday and began "shooting in the direction of our forces and was immediately shot and killed," Rosenfeld said. No Israeli forces died or suffered injuries in the exchange, he said.
Authorities did not immediately name the slain gunman. But previously, police identified the Tel Aviv shooting suspect as Nasha'at Melhem, 31, an Arab-Israeli from northern Israel.
On January 1, he allegedly sprayed more than 15 bullets from an automatic weapon
in "a number of different directions" near the Simta pub on Dizengoff Street in Tel Aviv, then fled, Rosenfeld said last week.
The police spokesman said authorities believe that in addition to the two deaths outside the pub, the shooter killed a taxi driver in Tel Aviv that day.
Uncle: Suspect had psychological disorder, was jailed before
The shootings came at a time of heightened tensions that have spiraled into violence in Israel and the Palestinian territories.
Authorities haven't indicated the January 1 shooter belonged to any militant group, nor have they offered details on his motivation -- including whether it was a criminal or terrorist act.
Melhem's father -- a volunteer for Israeli police -- recognized his son in surveillance video of the attack broadcast by Israeli media and immediately contacted authorities, Melhem's uncle told CNN.
The father discovered later that a weapon he kept in a safe at home was missing, the uncle said. It was not immediately known whether that weapon was used in the attack.
Ahmed Melhem said his nephew had a psychological disorder and had served time in prison for attempting to steal an Israeli soldier's weapon. It wasn't known if he was taking any medication.