Barcelona, who have won the last four editions of the competition and have lifted the prize a record 30 times, will host Real Madrid in the first leg on February 6, with the second leg coming on February 27 at the Bernabeu.
Betis will play at home to Valencia in the first leg and visit Mestalla in the second, with both ties being played on the same dates.
The final will be played at Betis’ Benito Villamarin in Seville on May 25.
Barca overcame a 2-0 deficit from their quarter-final first leg against Sevilla, thrashing the Andalusians 6-1 in the return leg to progress 6-3 on aggregate.
Real Madrid had a more comfortable path to the last four, beating Girona 4-2 at home and winning 3-1 away for a 7-3 aggregate win.
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.