Montreal police forensic investigator Caroline Simoneau told jurors Monday that her team searched through 31 garbage bags left outside the building in Montreal's Snowdon neighbourhood.
Among the trash, Simoneau said, investigators found human remains, a dead dog, knives and other items that were sent to a lab for analysis.
Magnotta has pleaded not guilty to five charges, including first degree murder, in the death of 33-year-old university student Jun Lin.
However, shortly after the trial began Monday, the judge told the jury that Magnotta had agreed to the facts in the case, including that he killed Lin.
He instructed the jury that their job now is to determine if Magnotta "committed the five offences with the required state of mind for each offence."
Magnotta's lawyer told the court he intends to prove that his client should not be held criminally responsible for his actions.
He said Magnotta suffers from schizophrenia and was hearing voices and feeling persecuted before the events took place.
In his opening statement, Crown prosecutor Louis Bouthillier told the jury he intends to prove that Magnotta spent six months planning the alleged murder before it was committed.
More than 60 witnesses are expected to be called during the six-week-long trial.
Lin's father, who travelled from China, said through his lawyer Monday that he intends to be present in court whenever possible to honour his son and find out the truth of what happened to his son.