"The first-team coach Philippe Montanier has informed Real Sociedad of his decision to reject the offer of a contract extension," La Real said in a statement .
"Therefore he will leave the club at the end of the 2012-13 season when his contract ends."
Real Sociedad are fourth in the standings and close to securing a place in Champions League qualifying for next season.
They said they would focus solely on their remaining two games, at home to Real Madrid on Sunday and at Deportivo La Coruna the following weekend.
"For that reason, Real Sociedad will make an announcement on this issue after the two remaining games," the club added.
Rennes subsequently released a statement confirming that Montanier would replace coach Frederic Antonetti, who had previously announced he was to step down.
"Philippe Montanier, the current coach of Real Sociedad, accompanied by his deputy Michel Troin, will succeed Frederic Antonetti as coach of Stade Rennais," read a statement on Rennes' website.
"They will join the group from Monday July 1."