The Blues will face the Swans in the penultimate round of the competition, while the Bantams are rewarded for their victory over Arsenal with an away tie against the Villans
The Blues enjoyed a convincing 5-1 win over Leeds in their previously postponed quarter-final, with goals coming from Juan Mata, Branislav Ivanovic, Victor Moses, Eden Hazard and Fernando Torres.
The game had been delayed due to Chelsea's involvement in the Club World Cup, with the west London outfit losing 1-0 to Brazilian side Corinthians in the final on Sunday.
Their opponents Swansea scraped through to the final four thanks to a 1-0 win over Championship side Middlesbrough at the Liberty Stadium, with a Seb Hines own goal giving the Swans the victory.
Bradford beat Arsenal on penalties at Valley Parade to win their ninth consecutive shootout and will face Aston Villa, who took a convincing 4-1 win away to manager Paul Lambert's former club Norwich.
The first legs will be played on the week commencing January 7, with the second legs during the week commencing the January 21.