Edward Stuart Muirhead-Smith, 56, was killed in the car park of the Max shopping centre in eastern Riyadh on Wednesday.
The Saudi Interior Ministry announced the slaying on Wednesday night, but did not give further details.
The British ambassador to Saudi Arabia, Sherard Cowper-Coles, condemned the killing calling it an act of terrorism.
"They should know - as the terrorists must know - that his murder will only make the British government more determined to stand with the Saudi government and people in the struggle against senseless terror of this kind."
Saudi media reported that two men in a white Toyota car shot the Briton four times in the car park and then fled.
Saudi Arabia has seen an increase
in the targeting of foreigners
The Saudi state-guided newspaper Arab News reported the same details on Thursday, adding that police were looking for two Saudi suspects and that Muirhead-Smith was shot in his car.
A spokesman for Marconi in Britain, David Beck, confirmed that Muirhead-Smith worked for the company.
Spate of attacks
There have been a spate of attack against foreigners in Saudi Arabia in recent months.
In May, two Britons were among six Westerners killed by armed men who sprayed gunfire inside an oil contractor's office in Yanbu, 350 km north of the Red Sea port of Jiddah.
Later that month, a Briton was among 22 killed in the shooting and hostage-taking in Khobar, an oil hub 400 km northeast of Riyadh.
BBC correspondent, Frank Gardner, was shot and seriously wounded in Riyadh in June. His Irish colleague was killed in that attack.
On Saturday, an explosion rocked the Saudi port city of Jeddah on the Red Sea near a branch of the Saudi-American bank.
Saudi Arabia has been hunting suspected al-Qaida fighters behind a series of bombings and shootings in the Gulf kingdom that have targeted the US-allied Saudi government, security authorities and foreign interests.