Unemployed Zakaria Bulhan, 19, targeted 64-year-old retired teacher Darlene Horton and several other random strangers on the evening of August 3 last year.
Within six minutes of the alarm being raised, armed police swooped on the scene and Bulhan was arrested without a shot being fired.
Initial fears of a terror attack were later calmed as it emerged that Bulhan's violent behaviour had been sparked by mental illness.
Teenager admits killing american tourist in russell square knife rampage
Unemployed Zakaria Bulhan, 19, targeted 64-year-old retired teacher Darlene Horton
On what would have been the first day of an Old Bailey trial, Bulhan denied murder but admitted manslaughter by diminished responsibility.
He also pleaded not guilty to five counts of attempted murder, but admitted wounding with intent to Martin Hoenisch, Lillie Selletin, David Imber, Bernard Hepplewhite and Yovel Lewronski.
The pleas were accepted by the prosecution.
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".
Mr Hoenisch, a retired fireman from Las Vegas, was visiting London with his wife, Laurie Kelly, when he was injured in the attack.
He said on Facebook afterwards that it was a "very unreal experience" and he was "still very saddened about the woman who was killed".
Miss Lewronski, 18, was visiting London from Tel Aviv when she was stabbed in the upper arm.
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Armed police swooped on the scene and Bulhan was arrested without a shot being fired
She said on Facebook she did not know whether to call it "luck or fate" that she escaped death, adding that she had watched as Mrs Horton "perished in front of my eyes".
Following the stabbings, a picture emerged of Bulhan as a "quiet, academic loner" who liked football, basketball and music.
The defendant is a Norwegian national of Somali origin who moved to the UK in 2002.
He lived with his mother and siblings in a council flat in Tooting, south-west London, and was a student at the local Graveney School.
MIss Horton was described as 'just one of the nicest, sweetest, family-focused people'
The court heard that Bulhan was suffering an "acute" episode of paranoid schizophrenia at the time of the attacks.
Prosecutor Mark Heywood QC said the case had been considered at the "highest level" and it was decided it was right to accept the pleas.
Mr Justice Spencer ordered attempted murder charges to lie on file.
Russell Square was the scene of one of the London suicide bombings in which 52 innocent people died on July 7 2005.