David Cameron paid tribute to Crown Prince Nayef for his "leadership and dedication" following the Saudi Arabian minister's death.
The Prime Minister said his thoughts were with the Saudi people, while Foreign Secretary William Hague sent his condolences to the kingdom.
Mr Hague said Prince Nayef, who was also deputy prime minister, served with "great dignity and dedication" and would be remembered for his contribution to the nation's prosperity and security.
The Saudi royal family said he died in an overseas hospital, though did not specify where, and confirmed he would be buried on Sunday after prayers.
Mr Cameron said: "My thoughts are with the Kingdom and its people at this time. I had the pleasure of meeting Crown Prince Nayef in January and was struck by the leadership and dedication with which he served his country for so many years."
Prince Nayef was elevated to the title in November 2011 after the death of his brother Sultan. A new crown prince will now be chosen from among his brothers and half-brothers.
Mr Hague said: "He served the kingdom for many years with great dignity and dedication and his contribution to the prosperity and security of the Kingdom will be long remembered.
"I would like to offer my sincere condolences to the Kingdom and its people at this sad time."