The 32-year-old appeared briefly in a Montreal court by video link from prison, where he is serving a life sentence for killing Lin Jun in May 2012.
Outside the courtroom, his defense lawyer Luc Leclair said: "We are not going on with the (appeal) process."
Leclair said Magnotta decided that he did not want to face a retrial.
"Facing 12 jurors again, facing the reporters, facing the same evidence, and having his whole life put out there... It's not a pleasant experience," he said.
The defense attorney also indicated that Magnotta was willing to meet with the victim's father "in the spirit of truth and reconciliation... And answer the father's questions perhaps."
"He wants to explain as much as he can his actions," he said.
After jurors returned a guilty verdict in December, Lin's father Diran said he hoped for an apology from Magnotta, "to see remorse" and "to learn what happened to my son that night."
He lamented to reporters that the proceedings had not provided "a true or a complete answer.
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