The decree did not specify when the embassy would be opened.
Lebanon and Syria decided to establish diplomatic relations, for the first time in their modern history, on August 13, during an official visit by the Lebanese president to Damascus.
Lebanon became an independent state in 1943, two years before Syria.
Lebanese Foreign Minister Fawzi Salloukh is expected to visit Damascus on Wednesday to discuss measures to be taken to finalize the establishment of bilateral relations.
Following the assassination of Lebanon's former prime minister Rafik Hariri in 2005, Syria gave in to international pressure and pulled its troops out of Lebanon, after almost three decades of military presence.
In addition to Hariri's death, anti-Syrian factions in Lebanon have blamed Damascus for a series of attacks targeting lawmakers and politicians opposed to Syria since 2005. Syria has denied any involvement.