An American woman found dead in her Florence apartment had been brutally beaten and strangled, Italian prosecutors said.

They suspect a Senegalese man she met at a disco who was detained after authorities received "decisive" DNA evidence from a condom and cigarette butt and he was found using her mobile phone.

Cheik Tidiane Diaw, a 27-year-old who had arrived in Italy from Senegal in recent months, was arrested early on Thursday at his brother's apartment and is being held on suspicion of aggravated homicide, Florence chief prosecutor Giuseppe Creazzo told a news conference.

Street-mounted security cameras and witnesses reported that Diaw and Ashley Olsen, 35, had left Florence's Montecarla nightclub in the early hours of January 8 and went to her home.

Once there, they had consensual sex. But sometime afterwards, Olsen's skull was fractured in two places with blows so violent they alone could have killed her, Mr Creazzo said. She was subsequently strangled.

Olsen's naked body was discovered the following day by her Italian boyfriend, who asked the apartment's owner to let him into the apartment because he had not heard from her in a few days, authorities said.

Mr Creazzo said Diaw had offered "substantially admissive" testimony in response to the accusations during a preliminary interrogation. Diaw has not been charged.

Police detained Diaw after DNA analysis came back from a used condom and cigarette butt found in Olsen's toilet, as well as biological samples taken from under her fingernails that belonged to Diaw, Mr Creazzo said.

Investigators matched that evidence with a DNA sample taken from a cigarette Diaw smoked while being questioned at the police station, prosecutors said.

Diaw was also tied to the crime because he had taken Olsen's mobile phone, put his own SIM card in it and used it, Mr Creazzo said.

"We have gathered serious indications of guilt against him," Mr Creazzo said, adding however, that a judge must confirm the arrest.

Mr Creazzo said Diaw had arrived in Italy illegally a few months ago to join brothers who had been there for some time. He told investigators he was working odd jobs, handing out flyers for local nightspots.

Mr Creazzo said the investigation continues but that no other suspects were at the scene of the crime. He said investigators had reached "a great point" in the investigation following the "decisive proof" from the DNA analysis.

Olsen moved to Florence a few years ago and was active in the expatriate arts scene. Her father, Walter, is a professor at a local design institute.