The American woman stabbed to death in London was the wife of a university professor from Florida who was just hours away from flying home.
Darlene Horton was visiting the capital with husband Richard Wagner, who was teaching summer classes, when she was attacked in Russell Square at around 10.30pm on Wednesday.
Florida State University said the couple had planned to return to their home in Tallahassee on Thursday.
The 64-year-old died at the scene and five other people were injured during the attack, suffering stab wounds.
A 19-year-old man, a Norwegian national of Somali origin who moved to the UK in 2002, remains in police custody. Sky News named him as Zakaria Bulhan from south London.
Florida State University (FSU) 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."
Florida Governor Rick Scott tweeted: "Extremely saddened to hear about the loss of Darlene Horton in London. Ann and I are praying for her family and loved ones."
Scotland Yard said no evidence has been found of radicalisation or anything to suggest the attack was "in any way motivated by terrorism".
Assistant Commissioner Mark Rowley said: "Whilst the investigation is not yet complete, all of the work we have done so far increasingly points to this tragic incident as having been triggered by mental-health issues.
"At this time, we believe this was a spontaneous attack and that the victims were selected at random."
Mr Rowley, Britain's most senior counter-terrorism officer, said armed officers arrived within six minutes of the call, adding: "The man was Tasered and he was detained." No shots were fired.
A British man who suffered a stab wound to his stomach in the attack remains in hospital in a "serious but stable" condition while an American man, an Australian man and woman, and an Israeli woman were all discharged from hospital on Thursday after receiving treatment for their injuries.
Witnesses described chaotic scenes in the wake of the attack.
A cyclist who was passing the scene moments after the stabbing told how he was flagged down for help by a Spanish family.
Fernando, 40, from Brazil, had not seen the attacker but said the family told police the man was wearing black shorts and a white shirt, and was covering his face as he made sweeping, stabbing motions.
He went on: "The moment the police arrived, they asked them if the man had been shouting. They said that he didn't say anything. They said that when he stabbed the people he didn't shout or scream anything."
Jodie Parry, who was in her hotel room when she heard a "commotion" in the street, told the BBC that the attacker ignored police as they screamed at him to stop running.
She added: "He was actually carrying a knife in his hand and he had blood on his hands."
Pol O'Geibheannigh, 45, was walking back from the cinema when he saw a massive police presence and a woman lying in a pool of blood.
He said: "That level of police presence I haven't seen since 7/7 and I was here - I live around the corner."
Matthew Barzun, US ambassador to the UK, tweeted his condolences following the attack.
"Heartbreaking news that a U.S. citizen was killed in #RussellSquare attack. My prayers are with all the victims and their loved ones," he wrote.
The attack took place in a popular tourist spot near the British Museum in Bloomsbury, and around a mile to the north of the bustling area around the Strand, where several theatres and scores of restaurants are located.
It came hours after Scotland Yard announced more armed officers would be deployed on public patrol around the capital after a spate of attacks in mainland Europe.
Met Police Commissioner Sir Bernard Hogan-Howe vowed to protect London, adding: "A normal night-out in our busy capital has ended in horrific circumstances."
London mayor Sadiq Khan called for the public to remain "calm and vigilant".