"We want to improve and strengthen the relations between Israel and Jordan," Vice Prime Minister Ehud Olmert said.
"I am very happy that we can make this gesture to honour the king of Jordan," he said about the move, approved by the cabinet at its weekly meeting.
Nine prisoners remain
A senior Israeli official said none of the nine prisoners to be released were involved in deadly attacks against Israelis, and they would probably be freed on Wednesday.
A Jordanian Foreign Ministry spokesman said earlier this month that Amman hoped most of the 18 jailed Jordanians would go free, but acknowledged that Israel was unlikely to release those involved in the killing of Israelis.
The Israeli official said of the nine prisoners remaining in custody, "eight have blood on their hands". He was referring to offences that included the killing of an Israeli soldier and membership in groups Israel regards as terrorist organisations.
"At this stage it was decided not to release them," he said, adding that one other prisoner would go free soon on completion of his jail term.
Jordan signed a peace treaty with Israel in 1994. Two months ago, it returned its ambassador to Tel Aviv for the first time in four years.
Since the start of a Palestinian uprising in 2000, several Jordanians have left Jordan to join Palestinian resistance groups that have carried out attacks against soldiers and civilians.
Many of the kingdom's people are of Palestinian origin.