According to the 1994 peace agreement, Israel was leased 405 hectares of land so that Israeli farmers could use the water-rich farmland for at least 25 years.
"Al-Baqoura and Al-Ghamr [the Arabic names] have always been our top priority, and our decision is to end Al-Baqoura's annexation and step away from the peace agreement based on our keenness to take whatever is necessary for Jordan and Jordanians", Jordan's King Abdullah II tweeted in Arabic on Sunday.
The premier said, "As part of the agreement between our two countries, Jordan kept the right to take back the two areas at the end of the 25-year period".
"Baqoura and Ghamr have always been at the top of our priorities and our decision is to terminate the annexation of Baqoura and Ghamr from the peace treaty is based on our commitment to take all necessary decisions for Jordan and Jordanians", the King said in an Arabic tweet.
"Baqoura and Ghumar are Jordanian lands and will remain Jordanian and we will exercise full sovereignty over our territory", the king said, according to a royal court statement. "These circumstances indicate that it is in Jordan's own interest to continue adhering to the peace treaty", he said.
It seems that the Jordanian leader is under an ongoing pressure from the country's parliament not to renew the leases and to return both areas to full Jordanian sovereignty.
There was no immediate Israeli reaction.
Former UN environmental official and critic of the Israel-Jordan peace treaty Sufyan al-Tell called the announcement "timely and reflects the will of the people of Jordan".
Baqura, in the northern Jordan Valley, was captured by Israel in 1950. "Historically speaking, the relationship between Israel and Jordan has existed for many years, and, simply put, Jordan can not exist without Israel".
Prime Minister Benjamin Netanyahu has not given up, saying Israel will negotiate the matter.
They have also been expanding economic ties in the past year including a major deal to export billions of dollars of Israeli gas to the kingdom through a pipeline that crosses their northern borders. Both are located on the border of Jordan and Israel. Activists and politicians have been vocal against a renewal they say perpetuates Israeli "occupation" of Jordanian territory.
During the peace negotiations, Amman allowed Israel to keep temporary control of Ghumar and Baqura - under the pretext that Israel had already built infrastructure and agricultural facilities in the areas - as long as it recognised they were sovereign Jordanian territory. The deal helped Amman to pave the way for USA economic and military assistance to the country.
Tensions between Israel and Jordan have mounted in recent months over such issues as the contested status of Jerusalem and its holy sites, stalled Mideast peace talks, and last year's shooting of two Jordanian citizens by an Israeli embassy guard in Amman, which ignited a diplomatic crisis.