The Scotland left back played a limited role for Arsenal last season and a change in system is likely reduce his playing time even further this term.
Tierney did not play any part in Arsenal's opening three Premier League games so far this season.
A £25m signing from Celtic in 2019, the 26-year-old had been linked with a move to Newcastle United but after confiding in Arsenal captain Martin Odegaard, Tierney has decided to pitch camp in Spain.
Odegaard spent a season on loan at Sociedad from Real Madrid in the 2019/2020 campaign.
Real Sociedad finished fourth in La Liga last season and will feature in the upcoming UEFA Champions League this term.
'Kieran Tierney has joined LaLiga side Real Sociedad on loan for the 2023/24 season,' confirmed an Arsenal statement.
'Everyone at Arsenal wishes Kieran all the best this coming season with Real Sociedad'.
‘My first impressions have been so good, everyone I meet have been so friendly, the city is so nice and the stadium is beautiful, Tierney said.
‘It is a big change [coming to La Liga] but something I am looking forward to so much.
‘It is an exciting challenge and I am delighted to be here.
‘Martin [Odegaard] said the fans and people are so good and really welcoming and you will love your time here.
‘The club is in a good place, especially over the last few seasons and this season the Champions League, so it is an amazing club.’
