Zakaria Bulhan, of south-west London, has been charged with the murder of Darlene Horton, 64, and the attempted murder of five other people.
Two women and three men were injured in the attack on Wednesday.
Mr Bulhan - a Norwegian national of Somali origin - appeared at Westminster Magistrates' Court.
He appeared without legal representation and sat hunched throughout the short hearing with his hand over his mouth.
As the names of the victims were read out in court he held his face in his hands.
When asked if he understood the charges, he nodded giving the judge a thumbs-up gesture.
Mrs Horton had been visiting London with her husband Richard Wagner, who was teaching summer classes.
Florida State University said the couple had planned to return to their home in Tallahassee on Thursday - the day after the attack.
The university's president, John Thrasher, said "there are no words to express our heartache".
A British man who suffered a stab wound to his stomach in the attack remains in hospital in a "serious but stable" condition.
An American man, an Australian man, an Australian woman and an Israeli woman were all discharged from hospital on Thursday, following treatment for their injuries.
Mr Bulhan was remanded in custody until 9 August.
A 19-year-old man charged with the murder of a US tourist in a knife attack in London's Russell Square has been remanded in custody.