Julie Reilly, 47, from Shieldhall Road in Govan, was reported missing on February 15 after failing to turn up to several appointments.
Earlier this week, Andrew Wallace, 41, was arrested over the death.
He appeared at Glasgow Sheriff Court charged with murder and attempting to defeat the ends of justice.
Detectives have now identified human remains found in the Govan area as those of Ms Reilly.
A Police Scotland spokeswoman said: “Detectives are continuing to search a number of locations in the Drumoyne and Govan areas.
“The response from members of the public has been very positive and encouraging and police have received numerous calls regarding suitcases and other items.
“All of these items are being thoroughly investigated, but in the vast majority of cases, they have turned out to be animal remains or other items unrelated to the investigation.
“The public should be aware that police activity will continue in these areas as part of the ongoing investigation and the public are encouraged to contact the police if they have any information or concerns.”