Zakaria Bulhan, 19, is accused of killing 64-year-old Darlene Horton of Tallahassee, Florida, according to a police statement.
Bulhan was also charged with five counts of attempted murder. He is expected to appear in custody at Westminster Magistrates' Court on Saturday.
Horton was married to Florida State University psychology professor Richard Wagner, who was teaching a summer session in London for the university.
The stabbings late Wednesday night rattled the city and came just hours after authorities announced an increased police presence
there following recent terrorist attacks across Europe.
Police said Bulhan is a Norwegian national of Somali origin, and "so far we have found no evidence of radicalization," Assistant Commissioner Mark Rowley said Thursday.
Norway's National Criminal Investigation Service said the suspect emigrated from Norway in 2002. It was unclear if he immigrated to the UK.
Rowley said the main line of inquiry is focusing on mental health issues, essentially ruling out terrorism as a likely motive.
Officials briefed on the investigation told CNN earlier that they believed the attack was terrorism, based on the initial evidence.
"Whilst the investigation is not yet complete -- all of the work that 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 the victims were selected at random," Rowley told journalists.
Stun gun used on suspect
Police said two other women and three men were wounded. The victims were from Britain, Israel, Australia and the United States.
Police were called after 10:30 p.m. Wednesday following reports of a man "seen in possession of a knife injuring people"
in central London's Russell Square, the Met Police said.
Officers used a stun gun on the suspect, and he was arrested less than 10 minutes later, authorities said.
Philippa Baglee told CNN she saw the aftermath of the attack when she went outside a bar to have a cigarette.
"I saw people standing over there looking at the ground. I could see someone laying down and a guy with a motorbike helmet balanced on his head just walking up and down," she said.
Russell Square, in the Bloomsbury district of west-central London, is a busy passing point in the daytime to some of the city's major attractions, including the British Museum and the main buildings of the University of London.
But it isn't particularly bustling at night compared with other nearby neighborhoods that are home to more restaurants and bars.
In the July 7, 2005, terrorist attacks in London
, the most devastating of the four bombs hit the Underground subway line running close to Russell Square. One of the bombs tore apart a double-decker bus in Tavistock Square, a few blocks to the north.
, Muhyadin Mire, 29, was charged with attempted murder after authorities say he carried out an unprovoked knife attack in a subway station in London's Leytonstone suburb.