Before starting to fire, the gunman is reported to have driven up in a vehicle from the Jordanian side to the Allenby Bridge crossing.
In a gunfight with Israeli security forces, he was slain.
Family members described him as a 39-year-old man from the southern Jordanian Huwaitat tribe, and the interior ministry of the nation verified that he was a citizen of Jordan.
The crossing manager stated that the three Israelis, who were all in their 50s, were shot at close range.
According to officials, it took place in a cargo area under Israeli supervision where Jordanian vehicles unload products before entering the West Bank.
According to the Israeli military, a terrorist arrived in the Allenby Bridge region from Jordan in a truck, got out, and started shooting at the Israeli security personnel stationed there.
Three Israeli citizens were declared killed in the attack, and the terrorist was taken out by the security forces.
The bridge has been closed until further notice, according to Jordanian and Israeli officials. Crossings adjacent to Beit Shean in the north and Eilat in the south have also been closed.