Diplomatic ties topped agenda at talks between Michel Sleiman and Bashar al-Assad.
The decree said that Damascus would open an embassy in Lebanon for the first time since independence.
Lebanon and Syria agreed to establish formal diplomatic relations during a visit by Michel Sleiman, the Lebanese president, to Damascus in August.
Lebanon’s foreign minister said that he would travel to Damascus on Wednesday to discuss the mechanism for establishing ties with his Syrian counterpart.
Syrian officials have said they expect ambassadors to be exchanged before the end of this year.
Friendship and co-operation
Syria’s official Al-Watan newspaper said that Damascus’ ambassador to Beirut would face a number of challenges such as “the cases of missing Syrians and Lebanese, border demarcation, and revision of certain accords”.
The two nations have been tied by a treaty of friendship and co-operation on political, economic and security issues since 1991, a year after the end of Lebanon’s 15-year civil war.
Lebanese critics of the so-called “brotherhood” agreement said it was heavily tilted in Damascus’ favour.
On Monday, George Bush, the US president, had told Syria that it must respect Lebanon’s sovereignty and urged Damascus to open full diplomatic ties with Beirut.
“I think that essentially the relationship between the two countries is the business of the two countries, and while I suppose there is pressure from the United States on Syria … the decision was a Syrian decision,” George Jabbour, a former Syrian MP, told Al Jazeera.
Bush’s warning came amid concerns over the deployment of 10,000 Syrian troops in the Abbudiya region along the border with its neighbour.
However, Sleiman issued a statement on Saturday saying that he accepted the soldiers were in place to tackle smuggling.
Syrian troops withdrew from Lebanon in 2005 after three decades of involvement in the country’s long-running political strife.
The move followed the assassination of Rafiq al-Hariri, a former Lebanese prime minister. A United Nations investigation implicated a number of Syrian security officials in the killing, a charge that Damascus has denied.