Chelsea, who thumped Leeds 5-1 on Wednesday night, will host Premier League rivals Swansea at Stamford Bridge in the first leg before heading to Wales for the second leg two weeks later.
Meanwhile, Bradford, who disposed of Arsenal in the quarter-finals, will host Aston Villa in the first leg at Valley Parade before heading to Villa Park for the return leg.
Interim Chelsea manager Rafael Benitez is targeting his first trophy at Chelsea following the draw.
Benitez saw his side beaten 1-0 by Corinthians in Sunday's final of the Club World Cup in Japan.
But the Blues showed few signs of jet lag as they came from behind to beat Leeds at Elland Road.
"It's a team that likes to play football, likes to play on the floor and also try to keep the ball so I think it will be interesting," Benitez told Sky Sports 1.
"Every competition is important for us; a top side has to try to win every competition and now we are in the semi-finals so we are close to winning."
Semi-final draw: Chelsea v Swansea, Bradford City v Aston Villa.
First legs to be played week commencing January 7 and second legs week commencing January 21.