Copies of the protocols said the border will reopen within two months of being ratified, the Reuters news agency said.
| Abdullah Gul, left, met Serzh Sarksyan, right met at a World Cup qualifier last year [EPA]
Turkey closed the border in 1993 as a political move in support of Azerbaijan, who was fighting Armenian-supported separatists at the time.
Some historians have estimated that 1.5mn Armenians were killed by Ottoman Turks at the end of the Ottoman empire.
Ankara rejects claims that the killings amounted to genocide, saying instead that Turks and Armenians were killed in high numbers.
The plan to normalise ties was initially announced in April amid warming relations.
Abdullah Gul, the Turkish prime minister, attended a World Cup qualifying football match between the two countries in the Armenian capital Yerevan and Serzh Sarksyan, the Armenian president, plans to make the return trip for a match in October.
But he had said that he wanted significant progress on the border issue first.
The rift has been an obstacle to Turkey's bid to join the EU and has antagonised Ankara's relations with the US.
The restoring of ties is expected to aid Turkey's regional influence and give Armenia access to Turkish and European markets.