British Prime Minister David Cameron urged Kenyans on Saturday to accept the decision of the Supreme Court to uphold Uhuru Kenyatta's election as president, a spokeswoman said.
In a letter to Kenyatta, Cameron offered his congratulations.
The prime minister "stressed that this represented the end of a remarkable process, in which more Kenyans than ever before turned out to vote", a Downing Street spokeswoman said.
"The PM urged the Kenyan people to be proud of the strong signal they have sent to the world about their determination to exercise their democratic right peacefully," she said.
"He encouraged all Kenyans to continue this spirit of peace and accept the decision of the court as final."
Kenya is still traumatised by the violence that erupted after the presidential election in 2007 which left more than 1,100 people dead, and over which Kenyatta himself is facing international charges of crimes against humanity.
Kenyatta was proclaimed winner of the poll on March 4 this year, but his rival Raila Odinga challenged the result.
In a ruling on Saturday, six Supreme Court judges upheld Kenyatta's victory and said the election had been conducted in a "free, fair, transparent and credible manner".
Cameron wrote in his letter that "the Kenyan people had made their sovereign choice, and resolved disputes through the rule of law and the strong institutions of the Supreme Court and due constitutional process", the spokeswoman said.
The premier said he now looked forward to working with Kenyatta's new government to build on the "deep and historic" relationship between Britain and its former colony.