The Boeing 727 was the airline's first scheduled flight from Syria to Iraq since the two countries broke off diplomatic ties in 1980 when Syria backed Iran at the start of the Iran-Iraq war.
The Syrian and Iraqi airlines subsequently closed the respective offices in each other's countries and ended connecting operations for more than two decades.
Syrian Arab Airlines is to make three weekly trips between Damascus and Baghdad, according to officials at the Damascus International Airport.
In September 2004, Iraqi Airways made its first flight to Damascus in 24 years but carried no passengers.
Since 1980, private charter flights have provided service between the two neighbouring countries.