The forward, who had been widely expected to join Madrid when his existing deal expires on June 30, has now signed a new three-year contract with PSG, the French champions announced Saturday.
Moments before the announcement, LaLiga released a statement confirming an ESPN report that the league would be filing a complaint over an alleged breach of finance rules.
"LaLiga will file a complaint against PSG before UEFA, the French administrative and fiscal authorities and European Union authorities to continue to defend the economic ecosystem of European football and its sustainability," the statement read.
"This type of agreement attacks the economic stability of European football, putting at risk hundreds of thousands of jobs and the integrity of the sport," it continued. "It is scandalous that a club like PSG ... can close such an agreement while those clubs that could afford the hiring of the player without seeing their wage bill compromised are left without being able to sign him. ... PSG is assuming an impossible investment, seeing that it has an unacceptable wage bill and large financial losses in prior seasons. It is violating current UEFA and French economic control rules."
Earlier on Saturday, LaLiga president Javier Tebas called PSG's renewal of Mbappe "an INSULT to football."
Tebas said on Twitter: "What PSG are going to do renewing Mbappe with large quantities of money (who knows where and how they pay it) after posting losses of €700 million in recent seasons and having a wage bill of over €600 million is an INSULT to football. [PSG president Nasser] Al-Khelaifi is as dangerous as the Super League."
Tebas has been an outspoken critic of PSG under owners Qatar Sports Investments -- a subsidiary of Qatar's sovereign wealth fund -- as well as the Abu Dhabi-backed Manchester City, describing their business models as "financial doping."
He has also attacked UEFA's FFP controls as being inadequate.
"What isn't understandable is that [PSG] are able to reject offers like the one they received for Mbappe," he said last September, after the Ligue 1 club had refused to sell the player to Madrid in the summer transfer window.
"The controls in France are failing. They're doing damage to the European market. UEFA's system is mistaken. We're going in the wrong direction."
Tebas and PSG president Al-Khelaifi became unlikely allies in their opposition to the European Super League after its attempted launch last year.
Tebas described the project as a "coup d'état" and "a joke." PSG refused the chance to join as one of its 12 founding members, with Al-Khelaifi leading alternative efforts at reform as new chairman of the European Clubs' Association.