Marco Rose's side produced a stunning fightback to win the second leg 4-1 on Thursday, having slipped 5-2 behind on aggregate in the 55th minute.
They will play the first leg against AS Roma at Anfield on Tuesday 24 April, before the return leg in Italy on Wednesday 2 May.
Atletico Madrid have confirmed that Diego Costa suffered a hamstring injury in Thursday's Europa League match against Sporting CP.
Atleti will hope to have the 29-year-old available for the first leg of their Europa League semi-final tie against Arsenal at the Emirates Stadium on April 26.
Atletico are the favourites to claim a third Europa League crown after progressing to yet another European semi-final.
"Everybody speaks about Atletico Madrid that they look the strongest team on paper, but you must say when you look at the results that Salzburg have done again".
"I am from France and Marseille are in there as well and that is always a hard place to go... maybe it is better that I don't wish for anybody".
Costa was a frequent tormentor of Arsenal in his three seasons with Chelsea, scoring in two victories over Arsene Wenger's side in the Premier League, and also helped get Gabriel Paulista sent off in a 2-0 win.
There is a lot riding on the Europa League for both sides. "So we play in it with enthusiasm", he added.