The man, identified as Diaw Cheik Tidiane, met Ashley Olsen in a local nightclub and the two had consensual sex in her home while under the influence of alcohol and possibly drugs, according to prosecutors.
The 35-year-old American was strangled in the early hours of Friday last week, Florence's chief prosecutor Giuseppe Creazzo told a news conference.
An autopsy also revealed she had two fractures to her skull, injuries that could also have proved fatal.
Mr Creazzo said Tidiane - a 25-year-old illegal immigrant - had "substantially admitted" the killing after police questioning.
Italian media has reported he told police he did not mean to kill Ms Olsen, but claimed she had fallen during an argument.
Surveillance video showed that Ms Olsen and Tidiane left the Montecarla nightclub and entered her house together, Mr Creazzo said.
Tidiane took Ms Olsen's phone and put his own SIM card inside it, he added.
The suspect's DNA was found under the woman's finger nails and on a condom and cigarette butt found in the house.
Tidiane is being held in a Florence prison and faces a charge of aggravated murder.
Ms Olsen, originally from Summer Haven, Florida, had been living in Florence for the last three years. She is thought to have moved there to join her father, Walter Olsen, who teaches in the city.
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