The shooting took place at the Allenby Bridge crossing between the West Bank and Jordan. Palestinian security officials identified the victim as 38-year-old Raed Zeiter.
Officials in Amman confirmed he also held Jordanian nationality.
The Israeli military claimed that troops had opened fire after Zeiter allegedly tried to snatch a weapon from one of the soldiers.
A Jordanian security official said that Zeiter worked as a judge in Amman and had left for the West Bank early on Monday.
The Jordanian justice ministry confirmed the information, saying he worked at a magistrates court in the capital.
Family members in Amman expressed shock over his death.
"My son is peaceful and professional. I am shocked," his 70-year-old father, Alaa Zeiter, himself a former judge said.
Palestinian security officials said he was originally from the northern West Bank city of Nablus.
Following the incident, the terminal was closed but later reopened, an Israeli official said.
RA/NJF