The Blaugrana are chasing their third consecutive Copa del Rey title and 29th overall, while Atletico have won the competition 10 times.
After a dominant 5-2 performance in the second leg against Real Sociedad, the defending cup champs Barcelona will face Diego Simeone and Atletico Madrid.
Barcelona will face Atletico Madrid in the semi-final of the Copa del Rey, with Alaves taking on Celta Vigo, the conquerors of Real Madrid.
Diego Simeone believes that Atletico Madrid's Copa del Rey semi-final opponents Barcelona are now the best side in the world.
Atletico were La Liga champions but lost the first leg of the 2015 semi 1-0 in Catalonia before an explosive return that featured 11 yellow and one red cards before Neymar's brace saw Barcelona win 3-2 on the night. We know them very very well. Find out who will meet each other in the semi-finals!
Meanwhile, Atletico reached this stage of the competition for the first time in three years after progressing 5-2 on aggregate against Eibar.
Celta, which ousted Real Madrid in the quarterfinals, is at home for the first leg against Alaves. Barcelona will be unlikely to play on that day, due to a Liga fixture on Sunday against Real Betis - their tie will take place on February 2 and February 9.
The final is to be on May 27 with the venue still to be determined, although Spanish media reported it will be at Atletico's Vicente Calderon, which is set to close at the end of the season.