A statement issued by Florida State University (FSU), where Mrs Horton's husband Richard Wagner works as a psychology scholar, said the couple were in London for a summer course.
They were due to return to the US today.
FSU President John Thrasher said: "There are no words to express our heartache over this terrible tragedy."
It comes after the 19-year-old arrested on suspicion of murder following the knife attack in central London was named by Sky sources as Zakaria Bulhan.
The victim has been named as 64-year-old American Darlene Horton
The Norwegian national, who is believed to suffer from mental health problems, remains in custody.
Sky's Crime Correspondent Martin Brunt said Bulhan is believed to be of Somali descent and emigrated to the UK in 2002 with his family
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