The young Magpies secured qualification into the knockout stages after progressing from Group C in second place, where they faced West Bromwich Albion, Hull City and Scunthorpe United and have been rewarded with a 734-mile round-trip to Devon.
Chris Hogg's side finished on 11 points after six games, one point behind West Brom, while Exeter advanced after an unbeaten run in Group D, which contained Doncaster Rovers, Aston Villa and Portsmouth.
The young Magpies will be aiming to replicate last season's memorable run in the tournament after reaching the Premier League Cup final before suffering a narrow defeat against Everton at Goodison Park.
Tickets for the Premier League Cup tie are priced at £5 for Adults and £4 for Seniors and Students, while under-18s can watch the game for £2.