It gave no details on the size of the deal and set no time-frame for the delivery of the new jets.
"Under the terms of the signed document Typhoon aircraft will replace Tornado Air Defence Variant aircraft and others currently in service ...," the embassy said on Wednesday.
The accord was announced after John Reid, the UK defence minister, met King Abdullah on Wednesday and after talks late on Tuesday with Defence Minister and Crown Prince Sultan bin Abdul-Aziz.
Sources close to the talks have said a deal is likely to involve Saudi Arabia buying at least 48 Eurofighter Typhoon jets, with an option to raise that to 72.
Analysts said the deal could be worth more than £6 billion ($10.6 billion).
Francis Tusa, editor of London-based newsletter Defence Analysis, said Typhoon jets had a unit cost price of about £65 million. Including weapons, support, training and other extras, a deal for 48 jets could total £6 billion ($10.6 billion). Including options, the deal could reach £10 billion, Tusa said.
Analysts at investment bank Morgan Stanley said the deal could be worth £7-8 billion to BAE.
London will also support Riyadh in developing what the statement called "a regional defence industrial centre of excellence".
The deal is a big boost for the
Reid said: ""This understanding is good news for both UK and Saudi industry.
"BAE Systems, as prime contractor, and its many UK subcontractors will benefit from the work envisaged under this understanding, which will help sustain several thousand UK jobs over the next 10 years."
The agreement is an important export order for the Eurofighter consortium, which recently lost out to US-based Boeing on a major deal to supply jets to Singapore.
In Europe, Eurofighters have been ordered by Britain, Germany, Spain, Italy and Austria.
Under the agreement, BAE Systems will also invest in local Saudi companies, develop a plan to transfer industrial technology and provide training for Saudi nationals involved in supporting military equipment.
The company already has a large number of personnel based in Saudi Arabia.