The 35-year-old's current contract was due to expire at the end of the season, but he will now remain at Anoeta until June 2016.
Arrasate - who previously served as assistant to Philippe Montanier before he joined Rennes in the close-season - is currently the youngest coach in La Liga.
"Real Sociedad has reached an agreement with coach Jagoba Arrasate to renew until June 30, 2016," read a statement on the club's official website.
"The previous agreement expired this summer."
Sociedad had been in contention to qualify again for the UEFA Champions League next season, but a run of one win in their past five league matches has all but ended the club's hopes.
Arrasate's men currently sit seventh in La Liga, with 51 points from 33 matches, 11 adrift of the Champions League places.
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
‘Ruben Amorim could have waited for Real Madrid and had a better chance to be successful – to have joined Manchester United, he must be convinced in his own ability’ Former Old Trafford coach’s verdict on new boss
