The Division Two encounter was due to kick-off at 1pm (GMT) on Monday, 22nd February but will now begin at 2pm at United's Little Benton Academy.
The young Magpies currently sit in 13th place, seven points adrift of the play-off spots, but can move above their Baggies counterparts with a victory at Fulham in their upcoming league fixture on Friday, 12th February.
The two sides last met in October, with Newcastle suffering a 1-0 defeat at West Brom's Training Ground following Tyrese Dyce's late winner.