The Glasgow giants were paired together in the draw for the last four, with Aberdeen facing Championship side Morton.
Premiership champions Celtic beat promoted Rangers 5-1 when the sides met earlier this month.
The semi-finals will take place on the weekend of October 22-23, with the final being played on November 27.
Celtic needed two late goals against Alloa on Wednesday to secure their place in the last four while Rangers, winners of the trophy by beating the Bhoys in 2011, eased past Queen of the South.
Morton are through to the semi-finals for the first time since 1979 while Aberdeen, last-gasp winners over St Johnstone on Thursday, are looking to regain the cup they won in 2014.
Source : PA
Source: PA