Earlier, Canadian Justice Minister Rob Nicholson confirmed Mr Magnotta was being brought home by Canadian military transport to face charges.
He was arrested in Berlin on 4 June.
Mr Magnotta is wanted for first-degree murder, defiling a corpse, threatening the prime minister and using the postal system to send "obscene, indecent, immoral or scurrilous" material.
'Swift and decisive'
"We're extremely happy with the result today," Montreal police commander Ian Lafreniere said.
"This is not the end of the investigation. We're missing an important part of the investigation, which is the head of the body."
Police said they would ask Mr Magnotta where the head is.
The suspect is to appear in court on Tuesday, Mr Lafreniere said. A lawyer is likely to be assigned to him then, the Quebec prosecutors' office told the Associated Press.
Montreal investigators said on Friday they had obtained a longer version of a video posted on internet which appears to show the murder.
In a statement Mr Nicholson said the suspect was in the custody of Montreal police as he thanked the German government "for their swift and decisive action in this matter".
Mr Magnotta did not oppose his extradition, according to German officials.