The former Lille and Nice manager left his Aiglons post at the end of last month after just one season in charge, during which he led the club back into Europe.
Galtier steered Nice to a fifth-placed finish in the 2021-22 Ligue 1 season, as well as reaching the final of the Coupe de France, which his side lost to Nantes.
However, Les Aiglons' push for Champions League football did not bear fruit, with Nice winning just six of their final 13 matches to finish fifth and settle for Europa Conference League football.
Galtier's relationship with the Nice board allegedly soured towards the end of the campaign, and director Julien Fournier opened the door for PSG to make their move.
PSG are now understood to have agreed an £8.6m deal to buy Galtier out of his Nice contract, and Les Aiglons have already replaced the 55-year-old with Lucien Favre.
Pochettino will be departing the Parc des Princes after just one-and-a-half seasons in charge, during which he won the Ligue 1 title, the Coupe de France and the Trophee des Champions.
However, the 50-year-old failed to lead PSG to Champions League glory, as Les Parisiens lost to Manchester City in the 2020-21 semi-finals before capitulating at the hands of Real Madrid in the last-16 this year.
PSG are thought to have made the decision to sack Pochettino a while ago, but the Argentine's departure from the club is yet to be confirmed as he negotiates a severance package with the French champions.
Galtier is said to have already visited PSG's training facilities, and the Frenchman could be ready to lead his first pre-season training session on Monday.
PSG reportedly offered Galtier a two-year deal with the option of an additional 12 months, but the publication adds that he will instead now sign a straight contract until 2024.
Galtier may be ready to face the media for the first time as PSG manager on Tuesday, and he arrives having won one Ligue 1 title and one Coupe de la Ligue crown as a coach so far.
Meanwhile, Pochettino leaves PSG after winning 56, drawing 13 and losing 15 of his 84 games in charge of the French club, and he only had 12 months remaining on his contract with Les Parisiens. body check tags ::