A Palestinian man drove the truck into a group of soldiers, in what police called a terror attack.
The victims are three women and one man, all in their twenties.
PM Benjamin Netanyahu said the attacker, who was shot dead by soldiers, was a suspected supporter of ISIS.
However, the prime minister gave no evidence to support the claim.
The victims were taking part in an educational trip, the Israeli military said.
The Israel Defense Forces (IDF) tweeted that their names were Lt. Yael Yekutiel, 20; Lt. Shir Hajaj, 22; 2nd Lt. Erez Orbach, 20 and 2nd Lt. Shira Tzur, 20.
The attacker, identified as 28-year-old Fadi Qunbar, came from the Palestinian district of Jabel Mukaber in east Jerusalem, near to the attack site.
CCTV footage showed the truck ploughing at high speed into the soldiers, before reversing over the victims.
The attack took place on the popular Armon Hanatziv promenade overlooking the walled Old City of Jerusalem.
In response, police spokesman Micky Rosenfeld said security had been heightened throughout Jerusalem.
An emergency meeting of the Israeli security cabinet approved administrative detention for ISIS sympathizers and authorized the destruction of the driver’s home.
PM Benjamin Netanyahu visited the site of the attack on January 8 and said: “We know that there has been a series of terror attacks.
“There definitely could be a connection between them – from France to Berlin, and now Jerusalem.”
The latest truck attacks took place during last year in Nice and Berlin.
The US state department condemned the attack “in the strongest possible terms” and the EU also issued a condemnation.
The Palestinian militant group Hamas praised the attacker. Hamas spokesman Abdul-Latif Qanou called it a “heroic” act and encouraged other Palestinians to “escalate the resistance”.
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