City's reward for their 1-0 FA Cup win at Boro on Saturday is a fourth round tie at Scunthorpe.
Former Chelsea and Celtic defender, Paul Elliott, and comedian and West Bromwich Albion fan, Frank Skinner, made the draw at Wembley Stadium.
It will be the second time this season that the sides have met. City defeated the Championship club 5-1 in the Carling Cup back in October.
Kick-off details and ticket news will be announced as soon as the television companies have selected their matches.
Ties will be played on the weekend of January 23.