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.
The Norwegian-born teenager, who is of Somali origin and moved to the UK in 2002, he also stabbed Martin Hoenisch, Lillie Sellentin, David Imber, Bernard Hepplewhite and Yovel Lewronski during the rampage before he was Tasered by police.
He pleaded guilty to manslaughter on the grounds of diminished responsibility and charges of wounding at the Old Bailey on Monday .
The Old Bailey heard how Bulhan's mental health was deteriorating in the days before the stabbings, and had been suffering an "acute" episode of paranoid schizophrenia.
Sentencing Bulhan, Mr Justice Spencer described the killing as "a tragic waste of life" and said the psychological effects on the survivors of the attack would never leave them.
He told Bulhan: "It is quite clear that when you committed these dreadful crimes you were not in your right mind. You were in the grip of mental illness."
Darlene Horton, the 64-year-old wife of a university professor from Florida, was just hours away from flying home when she was killed in the attack on Wednesday evening.
Retired teacher and keen tennis player Darlene Horton, 64 (pictured), was due to return to America today with her Florida professor husband Dr Rick Wagner but was stabbed to death by a Somali-born knifeman in the Russell Square attack.
An American woman has been killed and five people injured after a man with a knife attacked people in Russell Square, central London. The attack happened at about 10.30pm on Wednesday, near the British Museum.
A cyclist who was passing the scene on Wednesday night told how he was stopped by a family of Spanish tourists asking for help.
Fernando, from Brazil, said he called for an ambulance after seeing an “older woman” slumped against park railings with a stab wound to her back.
And it came on the very day Scotland Yard started putting 600 extra armed police on London's streets, including fast-reaction counter-terrorism teams on powerful motorbikes.