The borders between the two countries are poorly delimited in certain places, particularly the Shebaa Farms, a mountainous sliver of land rich in water resources located at the junction of southeast Lebanon, southwest Syria and northern Israel.
The 25-square km tract of farming land was seized by Israel from Syria in the 1967 Middle East war and is now claimed by Beirut, with the backing of Damascus. Israel says they are part of Syria.
Asked whether Thursday's agreement would include a redrawing of the Shebaa Farms, Walid al-Moualem, the Syrian foreign minister, said: "The definition of the Shebaa Farms cannot happen under occupation."
Lebanese and Syrian territories have also been in dispute over several areas of Bekaa and northern Lebanon since the creation in 1920 of greater Lebanon, an administrative district within the French mandate for Syria.
Human rights groups claim that around 650 people who went missing during the Lebanese civil war are being held in Syria, which dominated Lebanon politically and militarily for almost 30 years until April 2005.
Sleiman is the first Lebanese president to visit Damascus since Syria withdrew its troops from Lebanon in April 2005, two months after the assassination in a massive Beirut bomb blast of Rafiq al-Hariri, the former Lebanese prime minister.
Damascus has denied any responsibility despite accusations by Lebanese anti-Syrian groups.
Saad Hariri, Rafik al-Hariri's son and political heir, welcomed the establishment of diplomatic ties, describing it as an accomplishment for the Lebanese people.