"One of those convictions was his steadfast and passionate belief in the importance of the U.S.-Saudi relationship as a force for stability and security in the Middle East and beyond. The closeness and strength of the partnership between our two countries is part of King Abdullah's legacy."
The U.K. government also offered their condolences with Prime Minister David Cameron and Foreign Secretary Philip Hammond both releasing statements. The latter said that King Abdullah had served the kingdown for many years with "great dignity and dedication."
"His contribution to the prosperity and security of the Kingdom and the region will long be remembered," he added.
Meanwhile back at Davos, Former U.K. Prime Minister Tony Blair said that King Abdullah "was loved by his people and will be deeply missed," according to a statement.
Early on Friday morning, state television in Saudi Arabia confirmed that King Abdullah had died of pneumonia. He was admitted to hospital on December 31, state media reported at the time, and his brother Crown Prince Salman bin Abdulaziz has now succeeded him as the new ruler.
Saudi Arabia is the world's top exporter of oil and one of the biggest producers and the news is likely to mean investors will be keen to see what the succession means for the commodity which has fallen by over 50 percent since mid-June last year.
"I don't think a change of leadership in Saudi Arabia will have a long-term impact on the oil price," Mark Malloch-Brown, a special adviser for FTI Consulting, told CNBC in Davos.
Daniel Yergin, IHS vice chairman, added that while the succession was "orderly" and "well planned," geopolitical risk in the region was now something to watch.
"In terms of the oil price, it is remarkable that a year ago, politics was in the price and now there is no geopolitics in the price and some of that may come back."
Brent crude oil rose on Friday amid uncertainty following the death of King Abdullah. Brent futures were last trading at $49.27 a barrel, around 75 cents higher on the day while WTI crude futures were at $46.28, dipping 3 cents.
Major US ally
Saudi Arabia is seen as a major ally to the U.S. in the Middle East and in the immediate term there is unlikely to be any disruption in that relationship, according to Stephen Yates, the CEO of DC International Advisory.
Nonetheless, he told CNBC Friday that with any transition there are always questions.