The club, who are second in Ligue 1, had refused to pay money to the LFP in relation to French tax laws because they are based in a principality.
However, Monaco confirmed on Friday that a deal had been agreed that would involve them paying voluntary contributions to ensure they could continue to participate in the top flight, and the league's governing body released a statement on Saturday declaring their satisfaction with the outcome.
"The LFP and AS Monaco have signed an agreement protocol that definitively ends the dispute between them ongoing for more than a year," read the statement.
"Under the terms of the protocol, AS Monaco are definitively allowed to participate in the professional French championship while conserving their headquarters in the principality of Monaco.
"Out of concern for the equality and balance of the competition, AS Monaco are committed to paying a voluntary, fixed and definitive sum of €50 million to the LFP and will withdraw their plea to the Council of State.
"Both parties are pleased with the agreement reached."
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