The clubs have already met once this season at the Vitality Stadium, with the Cherries recording a first-ever victory over the Blues.
Incredibly, this will be our first ever meeting with Bournemouth in the FA Cup.
Our record against the south-coast club is 22 games played, 19 wins, two draws and one loss.
Goals Antoine Semenyo and Evanilson gave the Cherries a 2-1 win in November with Josko Gvardiol scoring a late consolation.
That loss ended a 33-game unbeaten run in the Premier League for the Blues who will now look to avenge that first ever defeat at the Vitality.
The FA Cup quarter-final matches will be played across the weekend of March 29/30.
Ticket details plus the date and time of the fixture will be released in due course.
Full draw
Fulham v Crystal Palace
Preston v Aston Villa
Bournemouth v CITY
Brighton v Nottingham Forest/Ipswich Town