The first leg of the tie will take place at Camp Nou on February 6 before the second leg at Santiago Bernabeu in the final week of February.
Lionel Messi and crew overturned a 2-0 deficit first encounter with Sevilla to a 6- 1 thrashing at the Camp Nou, making it a 6-3 aggregate score.
"If we are at our level we will go through", Barcelona director Guillermo Amor said. "Madrid always competes for everything, it is a great rival".
And Madrid were the last team to secure their semi-final berth last night, as the in-form Karim Benzema grabbed a second-leg double at Girona to help the 19-time winners make it through to the last four for the first time since 2013/14.
"There's nothing like it", said Real Madrid director Emilio Butragueno.
"There's nothing like playing in a Clasico".
"We are delighted with him for how he manages the squad and that is important because there are times when it is not easy to live with so many players of that level and that everyone is happy". "We are talking about two teams with a lot of resources, with extraordinary players, and we always expect very tight games".
Whilst it's true that Real will probably still be in the Champions League, they don't look strong enough to win it, so at this stage the Copa del Rey represents their best chance of silverware.
Real Betis play Valencia in the other semi-final, with the final on 25 May at Betis' home ground, the Estadio Benito Villamarin in Seville.
Betis meanwhile beat Espanyol 4-2 on aggregate, with Valencia overcoming Getafe 3-2 on aggregate by scoring twice in stoppage time in their 3-1 victory in the second leg at Mestalla.
"Valencia can expect to suffer because we want to play the final in our home", Real Betis executive Rafael Gordillo said after the draw.
Real Madrid's upcoming fixture list does not paint a prettier picture.