"I congratulate Muhammadu Buhari on his election victory as the next president of Nigeria and also President Goodluck Jonathan for the statesmanship he has shown in delivering free and fair elections and accepting the result," Foreign Secretary Philip Hammond said in a statement.
"It is now important for both parties to ensure the transition to a new government remains peaceful," Hammond said.
"Britain has a very deep relationship with Nigeria and we look forward to working with the new president, his government and the people of Nigeria in their aspirations for prosperity," he added.
The victory writes a new chapter in the country's often turbulent history after six military coups since independence from Britain in 1960 and 16 years of unbroken civilian rule by Jonathan's party.
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British Prime Minister David Cameron called Buhari on today to congratulate him on the "historic election win", according to a statement from his Downing Street office.
"The Prime Minister said that the UK would continue to support Nigeria, including by strengthening trade relations, and helping Nigeria to fight terrorism in the region and tackle corruption," a Downing Street spokesman said in a statement.