Argentina's two biggest teams drew the first leg 2-2 at Boca's La Bombonera on November 11 and were due to play the decisive second match at River's Monumental stadium last Saturday.
The second leg of the Copa Libertadores final between Boca Juniors and River Plate has been moved to the Bernabeu in Madrid.
Federation Internationale de Football Association had asked for the RFEF's help as they looked to solve how to move on with the final after both teams agreed not to play in Argentina after trouble marred last week's fixture.
River Plate have also been handed a £313,000 fine.
"In Spain we find the necessary tranquility.Madrid is the 10th safest city in the world and it has the largest Argentine community in Europe", CONMEBOL president Alejandro Dominguez said on Thursday.
Real Madrid's home will become the first stadium in the world to host four of football's five biggest trophies.
While CONMEBOL initially insisted the match would go ahead, the two sides' presidents agreed to postpone the second leg for 24 hours.
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Even so, it took great lengths before CONMEBOL postponed the match, and it tried to stage it a day later, even opening El Montumental and letting some fans in before ultimately heeding Boca's protests.
South American football's governing body CONMEBOL announced on Tuesday that the second leg would be played outside Argentina and they have now confirmed it will be held in the Spanish capital.
But Madrid won out, with Spain Prime Minister Pedro Sanchez tweeting that the country "is ready to organise the final".
"Spain is the country with the largest Argentine population outside of its country".
Both Boca and River accepted the proposal to play the game next month ahead of the Club World Cup, which the victor will take part in.
They have won the Copa Libertadores nine times between them.