The boy was found outside St Peter's Church, in Hough Lane, Bramley, on Wednesday morning. It is believed he had only recently been born before he was left by the doorstep.
He was taken to hospital by ambulance but was later pronounced dead.
West Yorkshire Police said the white baby boy was found in a Tesco bag for life.
The boy was wrapped in a towel and shirt.
Officers believe the mother could be in desperate need of medical attention and appealed for her to get in touch.
Det Ch Insp Nicola Bryar, of West Yorkshire Police, said: "We believe he was left at the vicarage sometime during the hours of darkness Tuesday into Wednesday and we would like to hear from anyone who was in the area and saw someone in the vicinity.
"The death of this baby boy in these circumstances is a real human tragedy and we need to establish exactly how this situation has come about."
A newborn baby who died after being left outside a church vicarage was abandoned in a supermarket carrier bag.