Rubaie said the resumption of flights between the two neighbours was "important", citing bilateral trade, tourism and "the size of the Iraqi community living in Syria".
The Syrian transport ministry welcomed the decision in a statement on its official Facebook page.
Most airlines stopped flying over Syria after the conflict broke out, with many taking longer routes to circumvent the war zone.
But the conflict has wound down in recent years, after major regime advances against rebels and jihadists with Russian military backing since 2015.
Damascus has been largely spared the violence.
"The agreement came on the principle of reciprocity, as SyrianAir crosses Qatari airspace and never stopped flying to Doha throughout the war," the Syrian transport ministry said at the time.
The use of Syrian airspace would see "increased revenues in hard currency for the benefit of the Syrian state", it added.
But the regime, backed by allies Russia and Iran, has since re-conquered much of the territory it had lost to rebels and jihadists, and now controls some two-thirds of the country.
Jordan reopened a key land crossing with its Syrian neighbour in October last year after a three-year hiatus.
Analysts said the move would help Syria inch its way back into trade with the wider region as it looks to boost its war-ravaged economy.
Jordanian officials have also visited Damascus to discuss plans to reopen Syrian airspace to its Royal Jordanian's commercial flights.
The Syrian conflict erupted in March 2011 with anti-government demonstrations that sparked a brutal regime crackdown.
The spiralling violence drew in regional powers and has killed more than 370,000 people, displacing millions.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)