Located in the Negev Desert south of the Dead Sea, the territory is called Tzofar in Hebrew and al-Ghamr in Arabic.
A military spokesperson said the lease had been extended with new terms through April 2020. Under the agreement, the territory was declared "a closed military zone" with access allowed only to farmers.
The Israeli foreign ministry was not immediately available to comment on the agreement.
A security officer with the Tamar Regional Council told the Hebrew-language news site of Ynet that Israeli farmers were entering the territory on Sunday morning to work the land.
The deal will expire in the spring, which coincides with the end of the agricultural season in the region, after which Israel will return the territory to Jordan.
Jordan previously denied that it had agreed to extend the lease.
Tzofar was supposed to be returned to Jordan on Saturday, together with Naharayim, or Baqoura in Arabic, a land in the Jordan Valley where the Jordan and Yarmuk rivers meet.
In the 1994 peace treaty between Israel and Jordan, Jordan agreed to let Israel lease both sites for 25 years.