Luka Magnotta, 32, was found guilty in the 2012 death of Jun Lin, 33, after eight days of jury deliberation.
He was also convicted on charges including committing an indignity to a human body, publishing and mailing obscene material as well as criminally harassing the Canadian prime minister and other lawmakers.
Radio-Canada, the French language arm of national broadcaster Canadian Broadcasting Corp, said it had confirmed Magnotta will withdraw his applications to appeal. A lawyer for Magnotta had been expected to appear in court on Wednesday to argue for the appeal.
In January, Magnotta's lawyer filed an appeal against all charges and is requesting a new trial, saying the judge erred in his instructions to the jury. The appeal also said the "verdicts are unreasonable and unsupported by the evidence and instructions."
Magnotta had admitted to killing and dismembering the engineering student in Montreal but pleaded not guilty on grounds of mental illness.
A first-degree murder conviction in Canada carries an automatic life sentence with no possibility of parole for 25 years.
The case gripped Canada in the spring of 2012 after Lin's body parts were found in the trash behind a Montreal apartment building and in packages mailed to political parties in Ottawa and to schools in Vancouver.
