Jamal Bakhit, 24, will appear before magistrates in Highbury Corner, London, on Monday accused of killing Rahmona Ahmedin, 23.
Her body was found on Wednesday by a lorry driver in a lay-by at Hinxton in the eastern English county of Cambridgeshire, police said.
The victim, who lived in London, had been stabbed and her body placed in a suitcase that was set on fire.
She had been reported missing on June 14.
A post-mortem examination gave the cause of death as a stab wound to the chest.
Bakhit was arrested on Friday after walking into a south London police station.
“He was no stranger to her, and we think that she was murdered in her home,” said a Metropolitan police spokesperson to news agency TT. Police believe that he may have been her boyfriend.
Police were unable to comment on whether Bakhit had confessed to the crime or how long the woman had been living in the UK.
“I can confirm only that it is a woman with a Swedish passport,” said detective inspector Phil Rickells of the Metropolitan police.
The Swedish foreign office were able to confirm later that the woman emigrated from Sweden four years ago.
British Interpol contacted the Swedish police on Friday seeking help to inform the murdered woman’s next of kin.
“They asked for our help to forward the news of her death to her family, and we have done so,” said Linda Widmark of the Swedish national police.