Chris Wilder's side moved impressively into the next stage of the competition with a 3-0 win against League One Blackpool on Tuesday night.
They will meet Steve McClaren's Premier League Magpies, who signed Ivan Toney from Town recently, in the week commencing 24 August 2015.
In recent seasons, Newcastle have come under fire from their own fans for not making a concerted attempt to win a major trophy, preferring to secure their Premier League status.
Whether that will change under McClaren remains to be seen with the first indication set to come against Northampton.