The airline said on Friday it had decided to resume services after introducing new security precautions.
The BA flights were grounded on 13 August after Britain's government warned it had received intelligence about a "serious threat" to air travel in the country.
"Our own team of security experts, together with British government officials, has worked closely with the Saudi authorities to implement a number of additional, robust and sustainable security measures," said BA's director of safety and security, Geoff Want.
"We are now satisfied that levels of security are appropriate for us to resume services."
The Times newspaper has reported British Airways had begun talks with Boeing, a leading US defence contractor, and European aircraft maker Airbus about installing anti-missile technology on its planes.
"We are talking with Boeing and Airbus about whether measures which are available on military aircraft could be transferred to civilian aircraft," Want told the daily.
"We are trying to understand the options but what might work for the military won't necessarily work on a civilian plane," he said.
BA normally operates four flights a week to both Riyadh and Jeddah from London Heathrow.
Flights to Riyadh will resume on Saturday and flights to Jeddah will restart on Sunday.
The UK has urged the Saudi authorities to crack down on anti-western groups in the kingdom for several years.
Following the anti-BA threats Saudi Crown Prince Abd Allah vowed Riyadh would defeat armed opposition activists.