Elliott Dickman's side secured their place in the knockout stages of the competition with a game to spare, finishing in second place of Group G on ten points.
United's reward is an away tie against the Cottagers, who won the Premier League 2 Division Two title last week, at Motspur Park on Friday, 4th March (kick-off 2pm GMT).
The two sides went head-to-head last month as Newcastle's second-string fell to a heavy 6-1 home defeat against the West London outfit.
The young Magpies will be aiming to complete another memorable run in the tournament after reaching the Premier League Cup final in 2019 before suffering a narrow 1-0 defeat against Everton at Goodison Park.