Fana television reported the news on its Twitter feed, saying the news was confirmed by Ethiopia's foreign affairs minister, Dr Workneh Gebeyhu.
"We salute the leaders, PM of Ethiopia Dr.Abiy Ahmed and President Isaias Afewerki of Eritrea for their courage and doing the right thing for their people of the two countries!"
It has been close to two decades since leaders of the two neighbouring countries have met.
After being cheered by crowds in Asmara, Eritrea's capital, and holding private meetings, the two leaders attended a dinner and announced new measures. Landlocked Ethiopia was left without access to Eritrea's ports on the Red Sea, while Eritrea lost its biggest trading partner and remained mired in poverty and a constant state of military readiness.
Ethiopia's refusal to implement the demarcation deadlocked relations between the two even after the end of a 1998-2000 boundary war that cost 80,000 lives.
The signing took place in Eritrea's capital, Asmara, before Abiy flew back to Ethiopia.
Ethiopia and Eritrea declared their "state of war" over on Monday and agreed to open embassies, develop ports and resume flights, concrete signs of a stunning rapprochement that has swept away two decades of hostility in a matter of weeks.
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"This historic official visit. heralds a new era of peace and cooperation", Eritrea's Information Minister Yemane Gebremeskel wrote on Twitter. "The yearning for peace was palpable and we will decidedly move forward for the good of our people", he wrote. He said the Ethiopian leader's visit was "history in the making" and had "set the tone for rapid, positive changes".
"Received the first call from Asmara in Eritrea!" exclaimed Ermiyas Teklu in Ethiopia, after speaking to his uncle and his family after more than two decades when telecommunications between the neighboring countries were blocked. Full-blown fighting ended in 2000, but their troops have faced off across their disputed frontier ever since. He did not identify which port.
Abiy said the two leaders have "agreed to bring down the wall between us".
Eritrea responded positively, sending a delegation to Addis Ababa last month for a meeting at which Abiy announced that Ethiopian Airlines would resume flights to Eritrea.
The global boundary commission later decided that Badme, a borderland that was a flashpoint of the conflict, belonged to Eritrea while it ruled that Eritrea should compensate Ethiopia for the huge amount of Ethiopian shipment confiscated in Assab Port.
Abiy has also pardoned dissidents, lifted a state of emergency and pledged to partly privatise key state-owned firms.
Across the border, Eritrea is one of the world's most isolated and repressive nations and has long used the Ethiopian threat to justify hefty military spending and long-term military conscription, which has caused hundred of thousands of young men to flee, mostly to Europe.
Ethiopia is the second-most populous country in Africa and an economic powerhouse, but Eritrea is one of the world's most closed and militarized societies, often compared with North Korea.