Galtier, who had a year remaining on his contract, is widely expected to be replaced on the PSG bench by former Barcelona and Spain coach Luis Enrique (53).
The club have called a press conference at their training ground for later on Wednesday when the new coach is set to be unveiled.
News of Galtier's departure from the Qatar-owned club had been expected ever since the end of the last Ligue 1 season at the start of June.
The former Saint-Etienne, Lille and Nice coach was appointed a year ago and led PSG to a French record 11th title.
However, they finished just a point ahead of runners-up Lens after losing seven games after the turn of the year.
Their league success was also overshadowed by a disappointing exit from the Champions League in the last 16 to Bayern Munich. PSG also went out of the French Cup at the same stage to Marseille.
In addition, the final weeks of Galtier's reign were marred by accusations that he made racist remarks about players during his previous job at Nice.
He has vehemently denied the accusations but will stand trial in December on charges of "moral harassment and discrimination on the grounds of actual or supposed membership or non-membership of a particular ethnic group, nation, alleged race or religion", according to prosecutors in Nice.
The offences are punishable by three years' imprisonment and a 45,000 euro (£38,500) fine.
