BAE Systems Chief Executive Charles Woodburn said the "memorandum of intent" is a step towards signing a full contract for the planes, with the company also having signed a £5bn deal to provide 24 jets to Qatar in December.
If finalised, the deal struck on the final day of the visit from Saudi Crown Prince Mohammed bin Salman would be a major boost for BAE Systems - which employs some 35,000 people in Britain.
News of the long-delayed deal came after both countries had set a £65 billion trade and investment target for the coming years, broadening a trading relationship built on defence and security.
But with the Saudi regime embroiled in a bloody bombing campaign in Yemen which has killed large numbers of civilians and precipitated a humanitarian crisis, the deal will anger anti-war campaigners.
On Thursday, UK and Saudi entities signed more than 18 economic agreements worth more than £1.5xbillion, covering education, pharmaceuticals and banking.
Leading the war is bin Salman, who is also Saudi Arabia's defense minister.
"Iran is playing a destructive and unsafe role in Yemen and destabilizing the region", British Foreign Secretary Boris Johnson told a news conference with his Saudi counterpart Adel al-Jubeir on Wednesday night.
Asked by Labour Party leader Jeremy Corbyn whether she would slam Riyadh's "shocking abuse of human rights", May said, "The link that we have with Saudi Arabia is historic, it is an important one, and it has saved the lives of potentially hundreds of people in this country".
May's government has remained defiant in the face of growing pressure to stop arms exports to Saudi Arabia, defending the sales amid evidence of war crimes and civilian deaths in Yemen.
Andrew Smith of Campaign Against Arms Trade said the United Kingdom had already licensed £4.6bn of arms for Saudi Arabia since hostilities began in Yemen in 2015.
"The Saudi government has formed an alliance to support the legitimate government in Yemen", Johnson said.