Los Blancos, whose president Florentino Perez has relentlessly championed the idea of a Super League, and promoters A22 Sports Management, were seeking $4 billion (£2.9 billion) in damages from European football governing body UEFA after the project collapsed.
"UEFA, the European Football Clubs (EFC, the sole, independent body representing football clubs within Europe) and Real Madrid CF reach an agreement for the good of European club football," read a statement published by Real Madrid and UEFA.
"This agreement of principles will also serve to resolve their legal disputes related to the European Super League, once such principles are executed and implemented."
Last week, Spanish giants Barcelona confirmed their withdrawal from the Super League, which was launched by 12 clubs in 2021 but quickly folded under the weight of immense fan and institutional pressure.