"The staff of the Saudi embassy arrived today in Baghdad," the official told AFP.
"They were met at the airport by foreign ministry officials. The staff consists of 35 people, led by the ambassador's deputy."
The ambassador himself is due to arrive by Thursday and will attend an official opening ceremony.
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A consulate is expected to open later in Arbil, capital of Iraq's autonomous Kurdish region.
Diplomatic relations between Saudi Arabia and Iraq were severed in 1990 but restored in 2004 after the US-led invasion toppled Saddam Hussein.
Relations remain strained between the Gulf kingdom, a Sunni powerhouse, and Shiite-dominated Iraq, where Iran and armed groups loyal to it wield huge influence.
Iraqi officials have repeatedly accused Riyadh of abetting the Islamic State group, which took over swathes of the country last year.