Chelsea will face Liverpool while Tottenham will play against League One side Sheffield United in the Capital One Cup semi-finals.
After Jose Mourinho's side and Sheffield United beat Derby County and Southampton respectively on 16 December, the Merseysiders secured qualification on 18 December with a 3-1 win against Bournemouth while Spurs thrashed Newcastle United 4-0.
Raheem Sterling responded to his critics following his missed chances against Manchester United at the weekend, excelling in the number nine role, scoring a brace to lead his side to victory.
Meanwhile, Lazar Markovic scored his first goal for the Liverpool since his summer move from Benfica, while Dan Gosling gained a consolation goal for Bournemouth.
Rodgers was happy with both the semi-final draw and the performance.
He said: "It will be a fantastic tie. If you want to win this competition, you have to play against the good sides.
"The most important thing was getting through, but our performance was brilliant. We're into the semi-final, it's over two legs and it didn't matter who we got. We needed to get there, it's Chelsea and we look forward to it."
In the other tie, Mauricio Pochettino's side booked their place in the semi-final with a comfortable victory over the Magpies at White Hart Lane.
An error from goalkeeper Jak Alnwick's earlier in the game paved the way to victory for Tottenham, allowing Nabil Bentaleb to open the scoring in the 18th minute.
Nacer Chadli scored the second just after half-time, while Harry Kane and Roberto Soldado completed the win.
Pochettino expressed his delighted after the game, claiming it "was the first time that there was the relation between the team and supporters".
"It was a fantastic night, a very good performance from the team. It was brilliant at White Hart Lane and I enjoyed it a lot tonight," the boss added.
The semi-final ties are set to be played on January 20 and 21 and January 27 and 28, with the final on 1 March. Chelsea and Sheffield will be away in the first leg.