The Magpies will face the Cherries - head coach Eddie Howe's former club - at St. James' Park on Wednesday, 21st December, with kick-off set for 7.45pm.
Seats for the fourth round tie initially went on sale to season ticket holders and Members, and sold out soon after going on full general sale.
A limited number of places remain in hospitality, starting from £120 per person.
The 51,660 crowd for the third round tie against Crystal Palace, which United won on penalties, was the club's largest ever home attendance in League Cup competition.
To purchase tickets for future matches, please visit book.nufc.co.uk or call the Box Office on 0344 372 1892.
Official ticket and hotel packages for all Newcastle United home Premier League and cup fixtures are available via club partners SportsBreaks.com. Packages include an official match ticket, plus a minimum one-night stay in a North East hotel, including breakfast.