Officers were called to Kimberley Road, Harehills, shortly before 3.20pm on Thursday June 23.
A woman's body had been found in bushes next to the boundary wall of the Asda store.
The body has now been identified as Theresa Jordan, known as Terri, who lived in Harehills.
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In a statement, her family said: "Beloved daughter, mother and sister who will be sadly missed.
"Gone but not forgotten. We will see you again, this is not where it ends. We will carry you with us until we see you again. Rest in peace.”
Police from the Homicide and Enquiry Team are investigating Terri's death, which is currently being treated as unexplained.
As part of the investigation, police have released a CCTV still image of Terri, taken on June 11, which is the last known image of her.
They want to speak to anyone who may have information that could help.
Detective Superintendent Sarah Jones, of the Homicide and Major Enquiry Team, said: “The last confirmed sighting of Terri was on June 11 and we are keen to speak to anyone who may have seen her after [that date], or has any information in respect of what she was doing after this time.
“We are also keen to speak to anyone who has been in the Kimberley Road area and witnessed anything suspicious or has information which may help with our investigation.”
Information can be given to HMET on 101 or online via the Live Chat, quoting reference 13220340197.
It can also be given anonymously to the independent Crimestoppers charity on 0800 555 111.