The Magpies reached the knockout stage by topping Group D, winning four of their six games in the group phase.
And their reward for qualifying for the latter stages of the tournament is a home tie against the Cherries, who finished second in Group C after being pipped to top spot by Wolverhampton Wanderers.
The draw was made on Thursday morning, and the full list of ties can be found below.
A date for the fixture will be confirmed in due course.
Premier League Cup last 16 draw
Newcastle United Under-23s v AFC Bournemouth Under-23s
Sheffield United Under-23s or Ipswich Town Under-23s v Derby County Under-23s
Middlesbrough Under-23s v Liverpool Under-23s
Brighton & Hove Albion Under-23s v Everton Under-23s
Aston Villa Under-23s v Blackburn Rovers Under-23s
Wolverhampton Wanderers Under-23s v Exeter City Under-23s
Swansea City Under-23s v Bristol City Under-23s
Southampton Under-23s v Leicester City Under-23s