Yordanos Brhane, aged 19 and originally from Eritrea, was found with multiple knife injuries at the house of multiple occupancy she lived in in Unett Street, Newtown, at around 7am on Saturday.
A 25-year-old man was arrested the following day in Stoke-on-Trent and has now been charged with her murder.
Alleged killer Halefom Weldyohannes, from Sheffield, is understood to be known to the victim.
He was due to appear at Birmingham Magistrates Court on Thursday.
Meanwhile the Independent Office for Police Conduct (IOPC) is investigating reports that it took officers almost an hour to get to the scene where Ms Brhane died.
A spokesman for the IOPC said: “We received a mandatory referral from West Midlands Police following the death of a 19-year-old woman in Newtown on Saturday. Our thoughts are with her family and those affected by her death.
“We will now assess the information available to determine the next steps.”
Detective Inspector Jim Mahon, from West Midlands Police's Homicide Unit, is leading the investigation.
He said: “We’re still working hard to try and understand what happened in the hours and days before Ms Brhane was found dead.
“If anyone knows her and has not yet spoken to us, or has information that may help our enquiry, then I would urge them to get in touch.”
The murder scene is still being held for further scientific examination.
Anyone with information should contact police online or by calling 101 quoting log 765 of 31/7. Alternatively information can be given anonymously to Crimestoppers on 0800 555 111.