Galtier left Nice on 27 June and is expected to replace Mauricio Pochettino at PSG.
The former Lille coach enjoyed a fine start to his single season in the south of France, with Nice flying high in Ligue 1 and embarking on a run to the Coupe de France final, beating PSG en route.
However, Nice was unable to keep up its push for Champions League qualification and ultimately had to settle for fifth place, while it was defeated 1-0 by Nantes in the Coupe de France final in May.
Nevertheless, Rivere is happy that Galtier has the chance to coach a star-studded PSG team, and believes the impending move suits all parties.
"I am very happy that Christophe has the opportunity to coach PSG and I will always keep a watchful eye on him," he said. "This alignment of the planets is good for everyone."
Galtier did not reportedly see eye to eye with Nice sporting director Julien Fournier, and Rivere conceded there were issues at the club.
"There were these tensions that should not have been expressed in the press," he said. "It may seem very confusing, but we analysed the situation calmly and I was able to explain my strategy to [INEOS director of sport] Dave [Brailsford].
"Nice must project itself with an offensive style, from the training centre to the first team. The pleasure we had at one time has been lost over the last three years."
Lucien Favre, who enjoyed success at Nice between 2016 and 2018, has been appointed as Galtier's successor.