The countries signed a letter of intent to finalise talks on a multi-billion-pound order for 48 Typhoon aircraft made by BAE Systems.
"Commenting on Friday's provisional deal announcement, the group said that this was a "positive step towards agreeing a contract for our valued partner".
As part of its Vision 2030 program, Saudi is modernizing its armed forces.
Saudi Crown Prince Mohammed bin Salman's visit to London will turn to defense and security on Friday as he meets British defense minister Gavin Williamson, touching on the most contentious element of his trip: arms sales.
Mrs May defended the UK's ties with Saudi Arabia earlier this week, saying all arms sales are strictly regulated.
In a similar thanks cable to the UK Prime Minister, Theresa May, HRH Prince Mohammed bin Salman hailed the establishment of the Strategic Partnership Council between the two countries, noting that the move confirms the determination of the two kingdoms to proceed with enhancing relations between them.
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.
However, the UK's opposition and aid sector have reacted angrily to the deal amid growing concerns over Saudi Arabia's war crimes in neighboring Yemen.
A final deal would not resurrect those jobs, the company said, but would provide continuing employment to 5,000 people working on the Typhoons....
Later this month Prince Mohammed, 32 will visit the United States, which also wants lucrative ties with the country.
BAE, Europe's biggest defence contractor, has long awaited a major Saudi order for Typhoons, and slowed production in 2016 to ensure it would remain competitive.
The Eurofighter Typhoon is the most important combat aircraft in BAE Systems' portfolio, accounting for almost a third of the unit's sales in 2016.