The clash - which will take place on January 31 or February 1 - will be the first time the Glasgow clubs have met since the financial collapse of Rangers in 2012.
Holders Aberdeen will face Dundee United in the other semi-final.
The last Old Firm meeting came in April 2012 when Celtic celebrated their title triumph with a 3-0 victory against a club that had been deducted 10 points and were battling for survival off the field
Charlie Mulgrew, Kris Commons and Gary Hooper scored the goals.
The last meeting between the teams in the League Cup was also the last time Rangers won a cup competition - Nikica Jelavic's extra-time winner giving them a 2-1 triumph at Hampden in 2011
Source : PA
Source: PA