The Frenchman, 48, is looking to guide Sociedad to a top-four finish in La Liga for the first time since 2003, with the club currently fourth in the standings, level on 62 points with fifth-placed Valencia, with two games remaining.
However, even the prospect of Champions League football with Sociedad next season was not enough to persuade Montanier to stay beyond his current deal which expires this summer, and he turned down the offer of a contract extension on Tuesday.
Montanier had previously been linked with Rennes and it was confirmed on Tuesday afternoon by the French club that he will take charge next season.
A statement on Rennes' official website said: "Philippe Montanier, 48 years old and the current coach of Real Sociedad, accompanied by his deputy Michel Troin, will succeed Frederic Antonetti as the coach of Stade Rennais FC.
"They will join the professional group to resume on Monday, July 1."
Sociedad confirmed earlier Montanier was set to leave.
A statement from the Spanish club read: "The coach of the first team Philippe Montanier has communicated to Real Sociedad his decision not to accept the offer to renovate (his contract) and, as such he will leave the club at the end of the 2012/13 season, when his contract ends."
Sociedad added that, in order to focus their energies on trying to finish fourth, they will wait until the end of the season before making any further comment on the situation.
Montanier took charge of Sociedad in 2011 after leaving Valenciennes and last season led the club to a 12th-placed finish.
Sociedad are at home to Real Madrid this weekend before finishing their campaign with a trip to Deportivo La Coruna.