The deal has been under discussion for years, but was snagged over the sides' disagreement over the place of the jets' production, with Riyadh wishing to have the jets partially assembled in Saudi Arabia.
The two countries agreed to finalize talks on a multibillion-pound order for 48 Typhoon aircraft, the fighter plane's maker BAE Systems said.
Last night BAE hailed the "positive step towards agreeing a contract for our valued partner".
"We are committed to supporting the kingdom as it modernises the Saudi Armed Forces and develops key industrial capabilities critical to the delivery of Vision 2030, BAE Systems said in a statement".
The memorandum of intent was signed after Saudi Crown Prince Mohammed bin Salman met with British defence minister Gavin Williamson.
The firm saw its share price rocket by almost three per cent on the news.
Before his visit, the 32-year-old Crown Prince talked about the importance of security ties between between the United Kingdom and Saudi Arabia.
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Saudi Crown Prince Mohammed bin Salman held a private meeting Thursday with Archbishop of Canterbury Justin Welby, where he made a "strong commitment" to interfaith dialogue, the archbishop's office said.
However, British arms companies are reported to have reaped huge benefits from the fighting, earning more than 6 billion pounds ($8.3bn) in trade with Saudi Arabia since 2015 - when the kingdom launched its massive aerial campaign against Houthi rebels.
The visit also brought agreement on an estimated £65bn worth of additional trade in the coming years as part of the Crown Prince's Vision 2030 economic plan.
Although May noted that she would raise humanitarian concerns about Yemen in his meeting with bin Salman, she stressed that all arms sales to Saudi Arabia were strictly regulated.
On Wednesday, the leader of the opposition, Jeremy Corbyn, criticised May and her government's lack of criticism of Saudi Arabia, arguing it was "colluding" in war crimes by selling arms to Riyadh.
The deal will be welcomed at Warton, Lancashire, where the swing-role combat aircraft are built by BAE Systems.