Officers discovered a body in woodland near to Middlewood Way on Wednesday.
GMP said they do not believe there are any suspicious circumstances surrounding the death, and a file will now be prepared for the coroner.
An extensive missing person investigation was launched by Stockport detectives, alongside a widespread search by specialist GMP officers.
Ch Supt Lewis Hughes said: “Our deepest condolences remain with Steven’s family and friends, who have been devastated by this traumatic news, we have officers supporting them through this difficult time.”
He said the search which involved the force’s Tactical Aid Unit, and canine and underwater units had been carried out in “challenging conditions and locations”.
“We hope today’s discovery provides some answers for Steven’s loved ones,” he added.
