Madrid eased past their age-old rivals 4-2 on aggregate in the semi-final thanks to a 3-1 win in the Camp Nou that also ended Barcelona's 22-match unbeaten stretch at home.
Frenchman Varane, who joined Los Blancos from Lens in summer 2011 and is still just 19 years old, scored the third tonight after Cristiano Ronaldo's opening brace.
"In my opinion, Varane showed again today what a great defender he is. Well done to him," tweeted Kompany, 26.
Madrid will go on to face either Atletico Madrid or Sevilla in the final. The former lead 2-1 after the first leg and are favourites to progress and set up a Madrid derby final.