Magnotta appeared before the Quebec Court of Appeal via video conference from jail on Wednesday.
A judge asked him if he was dropping his appeal voluntarily, and Magnotta replied yes.
The withdrawal of the appeal comes a day after CBC reported on the impending move.
In December, a jury found the 32-year-old guilty of the 2012 first-degree murder of Lin, a Chinese national who was studying engineering in Montreal.
Magnotta was also found guilty of:- Committing an indignity to a body.
- Publishing obscene material.
- Mailing obscene material.
- Criminal harassment.
Magnotta admitted to committing the acts, but Leclair argued he should have been found not criminally responsible because of mental-health issues.
Leclair had filed two appeals in January seeking a new trial.
Both were dropped on Wednesday.
One appeal cited judicial errors, and another was seeking leave to appeal on a number of other issues.
Jun Lin's family 'rebuilding their lives'
Daniel Urbas, the lawyer representing Lin’s family, said the victim’s mother, sister and father were notified through a translator in China that the appeal had been dropped.
“They're going to be proceeding now, rebuilding their lives with the money that's been collected and will continue to be collected on their behalf,” he said.
More than $70,000 Cdn has been donated to the family to help with some of the costs incurred in the wake of Lin's murder, including their travels to Canada for the court proceedings.
Urbas said Lin’s father, Lin Diran, remains steadfast in his desire to hear an apology from his son’s killer.
“He wants to hear something — some kind of response, remorse from the killer of his son — and he would like to learn more about what happened that night and how it came to happen,” Urbas told reporters outside the Montreal courthouse.
Magnotta did not testify in his own defence, nor did he address the court during his sentencing.
The first-degree murder charge carries a sentence of life imprisonment with no chance of parole for 25 years.