Prime Minister Theresa May said police were still hard at work investigating the source of the nerve agent.
Police identified her after the information was released to family and friends.
Laboratory tests previously confirmed that Sturgess and the man were exposed to the nerve agent after touching a contaminated item with their hands.
"This is shocking and tragic news", Neil Basu, Britain's most senior counter-terrorism officer, said in a statement. May also said her "thoughts and condolences" go to Sturgess' family and loved ones. Hours later, emergency workers responded to the same address after the 45-year-old man had fallen ill, police said.
"This bad news has only served to strengthen our resolve to identify and bring to justice the person or persons responsible for what I can only describe as an outrageous, reckless and barbaric act", he said.
Canada retaliates, starts tariffs against the US
Trudeau reiterated that he "had no choice" but to announce retaliatory tariffs, according to the prime minister's office. NDP Leader Jagmeet Singh said he didn't know if anyone should be surprised that Trump made a comment of that nature.
Dawn Sturgess, 44, has died.
The hospital's medical director, Christine Blanshard, told the BBC that hospital staff worked tirelessly to save Sturgess.
But, they say, "it is important that the investigation is led by the evidence available and the facts alone".
"The Government is committed to providing full support to the local community as it deals with this tragedy", she wrote in a second tweet.
Home Secretary Sajid Javid said he is "determined to bring the killers to justice".
Britain's public health authority acknowledged on Friday the concerns of people living in the area after the two incidents involving Novichok, but said it was confident that the risk to the public remained low.
Trade tensions starting to affect global economy
On Thursday, US President Donald Trump warned that the US may ultimately target over $500 billion worth of Chinese goods. And Beijing's tactics may go beyond tariffs to include arbitrary quarantines and a costly uptick in customs inspections.
Those locations are Muggleton Road, Boots pharmacy and the Baptist church in Amebsury, and John Baker House and Queen Elizabeth Gardens in Salisbury.
Dawn Sturgess died after exposure to a nerve agent in southeast England.
Russian authorities denied any involvement.
Police are still trying to piece together how Ms Sturgess and Mr Rowley came into contact with Novichok.
Police say the nerve agent that sickened Rowley and Sturgess was the same type that nearly killed the Skripals, but scientists haven't been able to tell whether it was from the same batch.
Credits Scene For Ant-Man and the Wasp Leaks Online (SPOILERS)
Obviously, part of Avengers 4 is going to have to deal with Scott either getting out of or going further into the Quantum Realm. We can confirm that there are TWO additional scenes after the credits, so make sure to stay in your seats until the very end.