Moe Maraachli and Sana Nader, parents of the 14-month-old boy, have been engaged in a battle with doctors at Ontario's London Health Science Center, Postmedia News reported Monday.
Baby Joseph has a severe neurological condition doctors at the Ontario hospital said is fatal and they decided to remove his breathing tube.
The baby's parents objected, saying they believe removing the tube would cause him to choke and die violently.
They want Joseph to receive a tracheotomy, which would open his airway and allow him to die at home.
Joseph's parents fought the hospital's decision in a Canadian court last month, but the court ordered them to consent to the withdrawal of the breathing tube, at which point the parents sought to have the child transferred to the United States.
The U.S. group Priests for Life said it would pay the full costs of Joseph's transfer and all medical expenses in the United States, Joseph's aunt Faith Nader said.
The St. Louis hospital confirmed Joseph's arrival Monday.
"Our physicians are examining Joseph to determine the best course of action," Bob Davidson, a spokesman with the SSM Cardinal Glennon Children's Medical Center, said.
Celebrity Families of 2014 [PHOTOS]