Rovers - Premier League champions in the 1994/95 season - beat League Two Wrexham 4-1 at Ewood Park on Monday night to set up a home tie against the Magpies, who reached the last 16 for only the second time in 18 years with Saturday's 2-0 win at Fulham.
Managed by former United forward Jon Dahl Tomasson, Blackburn are currently 18th in the Championship and beat Cambridge in the third round before a brace from Sammie Szmodics and goals from Sam Gallagher and Sondre Tronstad saw off Wrexham.
Eddie Howe's side beat local rivals Sunderland 3-0 in the third round, with Alexander Isak scoring twice following a Dan Ballard own goal at the Stadium of Light, before Sean Longstaff and Dan Burn were on target at Craven Cottage at the weekend.
Blackburn, like Newcastle, have lifted the cup six times in their history.
The fifth round will be scheduled during the week commencing Monday, 26th February and fixture details and ticket news will be confirmed on nufc.co.uk in due course.
The full FA Cup fifth round draw is:
Blackburn Rovers v Newcastle United Chelsea or Aston Villa v Leeds United or Plymouth Argyle AFC Bournemouth v Leicester City Liverpool v Watford or Southampton Bristol City or Nottingham Forest v Manchester United Wolverhampton Wanderers v Brighton & Hove Albion Sheffield Wednesday or Coventry City v Maidstone United Luton Town v Manchester City