Unemployed Zakaria Bulhan, 19, targeted 64-year-old retired teacher Darlene Horton and several other victims on the evening of August 3 last year.
The defendant, from Tooting, south west London, was charged with murder and the attempted murders of Martin Hoenisch, Lillie Selletin, David Imber, Bernard Hepplewhite and Yovel Lewronski.
Bulhan today admitted the manslaughter of Horton during an appearance at the Old Bailey.
He is a Norwegian national of Somali origin who moved to the UK in 2002.
Mother-of-two Mrs Horton was visiting London with her husband, Richard Wagner a university professor from Florida who was teaching summer classes. She was due to return to their home in Tallahassee the following day.
She was described by a neighbour as "absolutely lovely" and "just one of the nicest, sweetest family focused people".
Florida State University said the couple had planned to return to their home in Tallahassee on Thursday.
University president John Thrasher said: "There are no words to express our heartache over this terrible tragedy.
"We are shocked that such senseless violence has touched our own FSU family and we will do all we can to assist Professor Wagner and his loved ones, as well as his friends and colleagues in the psychology department, as they mourn."