Presented by John Fendley, co-presenter and footballing icon Jimmy Bullard will be selecting the ties alongside actor and Leyton Orient fan Danny Mays.
Leeds United were the last Yorkshire side standing in the competition but were knocked out by Arsenal at the Emirates Stadium on Tuesday evening.
Former Hull City midfielder Jimmy Bullard said: “I’m absolutely buzzing to be making the draw, it’s a real honour.
"One the proudest moments in my career was playing in the League Cup final in 2006 with Wigan Athletic.
"Even though the result didn’t go our way, to play in a Cup Final in front of all of my family and almost 70,000 fans was a very special occasion.”
Chelsea and Sunderland were the other two clubs who reached the last eight on Tuesday night with Liverpool, West Ham United - who knocked out holders Manchester City on penalties - Spurs, Leicester City and Brentford making up the rest of the quarter finals.