Police say the man went to a home in a neighbourhood in the city's North End on the afternoon of Oct. 20 to turn the kids over to a relative, found no one at home and simply left the kids on the stoop.
"A concerned citizen contacted police," Winnipeg police Patrol Sgt. Monica Stothers said Friday.
"Police were in attendance for several hours and the male did not return to check on the welfare of the children and no other person attended to the residence."
It was raining at the time and the temperature was eight degrees and falling. The kids, both of whom are under two, were taken care of and were unhurt. Ten days later, a 24-year-old man turned himself into police, Stothers said.
Police have no idea why the man walked away from his kids, she said.
"I don't know what he was thinking. His actions were absolutely irresponsible."
Police have not released the man's name because charges — two counts of child abandonment —have not yet been formally laid.