Friday's agreement to the long running dispute means Monaco will escape France's new 75 percent super-rich tax rate.
The LFP in March 2013 issued Monaco with an ultimatum — telling the Ligue 1 side to move their registered company across the border into France by June 2014 or risk getting kicked out of the French league.
The dispute arose as French clubs felt Monaco received considerable financial advantages falling under the less onerous tax regime of the Principality.
Friday's deal comes ahead of a scheduled Council of State hearing next week to rule on the affair.
Confirming the settlement the LFP declared: "Monaco have agreed to pay a voluntary…and one-off sum of €50 million to the LFP and have stopped their action before the Council of State."