The Under-20 World Cup gets under way later this month, with former Magpies coach Paul Simpson and his Young Lions squad set to face Argentina, Guinea and the hosts Korea Republic in the group stage.
Goalkeeper Woodman, 20, is included after enjoying a solid half-season on loan at Scottish Premiership side Kilmarnock, where he made 15 appearances after joining along with fellow United players Sean Longstaff and Callum Roberts in January.
And forward Armstrong, also 20, is named after spending almost the whole campaign on loan at Sky Bet Championship side Barnsley, where he played 35 times, scoring six goals.
The pair begin their bid for World Cup glory at the Jeonju World Cup Stadium against Argentina on Saturday 20th May, before facing Guinea there three days later.
England then face Korea Republic in Suwon on Friday, 26th May in their final Group A game.