Charge d'affaires Fahd al Qahtani will look after the embassy until a new ambassador is appointed, the report said.
"We are keen to extend all possible support to the interim Afghan government," Qahtani told the news agency.
Saudi Arabia was one of the three countries that recognized the former Taliban regime in Kabul. The other two, Pakistan and the United Arab Emirates, have also recognized the new Afghan government that replaced the Taliban in December last year.
Establishing full diplomatic relations will boost the image of the interim administration in Afghanistan since -- as the custodian of Islam's two holiest places -- Saudi Arabia has a special significance in the Islamic world. Thousands of Afghans visit Saudi Arabia every year for the annual Hajj pilgrimage.
New relations will also allow the cash-starved nation to send its workers to Saudi Arabia where hundreds of thousands of people come to work from impoverished Muslim countries.