The border crossing, known as Jaber on the Jordanian side and Nassib on the Syrian side, was a key trade route before Amman closed it after the post was overrun by rebels in April 2015.
"This was a crucial artery of trade between Jordan and Syria and transit to other countries", said Jordanian government spokeswoman Jumana Ghunaimat.
Syrian government troops recaptured it in July, after rebels reached an agreement with Russian mediators to end the violence in the southern province of Deraa and surrender the crossing.
The business owner requested anonymity, fearing reprisals back home in Syria.
"How could any conditions be imposed on the Lebanese side for the crossing of Lebanese trucks at a time when crossings at the Syrian-Lebanese borders take place normally without any preconditions?" the sources said.
The Syrian government began repairing its side of the border crossing in mid-September, Syrian state news agency SANA reported at the time.
The Assad regime retook the area around the border crossing at Naseeb in July during a weekslong Russian-backed offensive to drive opposition groups from their stronghold in southwest Syria.
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On the Syria-Jordan border Monday morning, several cars bearing Jordanian license plates queued to enter Syria as travellers expressed their joy at being able to cross the border.
Israel captured much of the strategic Golan plateau from Syria in the 1967 Six Day War and later annexed it in a move not recognized by the global community.
There are also signs that Syria is attempting to open up crossings with other neighboring countries in the wake of Naseeb. The UNDOF deployed in the area in 1974.
The US-led coalition has spread flayers over the Hajin enclave, east of the Euphrates river, in which it called the area's people to leave it, in sync with the battles against the "Islamic State" (ISIS).
On Saturday, Isil militants stormed a settlement for displaced people in Hajin and abducted scores of civilians.
The Syrian Foreign Ministry on Sunday called for an global investigation into the "crimes" of the USA -led coalition, following a recent attack with white phosphorus in Deir al-Zour, said local news agency.
He says terrorists used to control [Syria's] border crossings and the countries that supported these groups wanted to keep the crossings closed.
Omar Abou Leila, a Deir el-Zour native residing in Europe who runs the Deir el-Zour 24 news network, said the militants also abducted SDF fighters. But the observers left the crossing as Syria's civil war made it unsafe.