Police say they're satisfied that the intoxicated 19-year-old wandered into the wrong house by mistake, believing he was at a friend's residence, and played down the fact that he left a note near a collection of knives.
Trudeau was out of town when the incident happened, but his wife and children were asleep upstairs.
The police say an individual came forward after they released video footage of a suspect.
They say the man has been cautioned and the case is closed.
Nothing was taken in the incident, although a note was left — alongside a collection of knives — saying doors should be locked at night.
At a police news conference, police said the man briefly considered taking items from the home, including the knives and an electronic device, but reconsidered and instead simply left the knives near his note.
A Trudeau spokesman didn't comment on the fact that the man wasn't charged, saying it was a matter for police to decide.
"We fully respect the Ottawa Police Services' responsibility to make this determination," the spokesman said.