The land was leased for a 25-year renewable period under annexes of the 1994 accord that lay down a one-year notice period.
Responding to the announcement, Israel's Prime Minister Benjamin Netanyahu said he meant to "negotiate with Jordan for its extension" adding that "there is no doubt that the entire agreement is important and dear to both our countries".
"Al-Baqura and al-Ghamr have always been our top priorities and our decision is to end their extension from the peace agreement based on our keenness to take everything necessary for Jordan and Jordanians", the king tweeted on Sunday.
There was no immediate Israeli reaction.
The decision was met with exuberance from Jordanians, for whom the peace treaty has become deeply unpopular over Israel's reluctance to follow through on water-sharing agreements, restrictions on Jordanian trade with the West Bank, and most of all what many see as a violent occupation of Palestinian territory and the denial of basic rights and self-determination to Palestinians.
But he said Israel "will enter negotiations with it on the possibility of extending the current arrangement".More news: Mega Millions Jackpot Climbs to $970 Million
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Earlier this month Jordan's newly appointed ambassador to Israel, Ghassan Majali, arrived in the country and presented his credentials at the Foreign Ministry, taking a step toward restoring ties between the shaky allies.
Meanwhile the Yediot Aharanot newspaper quoted Eyal Bloom, a local official in southern Israel, as saying that the Tzofar area was important for Israel's security and 30 Israeli farms would collapse if Jordan reclaimed it. They have also been expanding economic ties in the previous year.
In response to the move, Prime Minister Benjamin Netanyahu pledged, as cited by Haaretz, to try and talk Jordan into extending the lease. The armistice after the 1948 war stated that the land was in Jordanian territory, and not what is now modern-day Israel. An incident past year in which an Israeli security guard killed two Jordanian citizens within the Israeli embassy compound added to the tension.
Under the treaty, Israel retained private land ownership and special travel rights in Baquora in the northwestern part of the kingdom and Ghumar in the south.
"There is an extensive range of agreements between Israel and Jordan", he said. Baker, who was part of the team that negotiated the treaty with Jordan, said Israel also allows Jordanian trucks to use Israel's ports. However, Israel-Jordan relations have been strained in recent years, particularly due to Amman's stance on the issue of Jerusalem.
Relations between Jordan and Israel deteriorated a year ago when an Israeli security officer shot and killed two unarmed Jordanian men in the Israeli embassy in Amman.