According to the police, the 19-year-old Norwegian citizen is of Somali descent and moved to Britain at the age of five.
He was also charged with five counts of attempted murder, in relation to the five other individuals who were injured, the police said in a statement.
He will appear in custody at Westminster Magistrates' Court on Saturday, it added.
Police raided his home in Tooting, south London, on Thursday after he was arrested on suspicion of murder.
The police said they received numerous calls starting at 10.30 p.m. on Wednesday describing a "man attacking people with a knife" between Russell Square, Montague Street, Bloomsbury Square and Great Russell Street.
Bulhan was arrested at the scene after police stunned him with a Taser following the attack, near the Imperial Hotel and the British Museum. The suspect was taken to a south London police station after receiving treatment in hospital.
Horton and her husband Richard Wagner were in London for a summer course and were due to return to the United States the day after the fatal attack.
Florida State University, where Wagner is a psychology scholar, issued a statement saying: "There are no words to express our heartache over this terrible tragedy."
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