Euro 2024 winner Zubimendi had previously been a target for Liverpool and was also linked with Real Madrid.
“This is a huge moment in my career,” he said. “It’s the move I was looking for and one I wanted to make. As soon as you set foot here, you realise how big this club and this team are.
“I set my sights on Arsenal because their style of play is a good fit for me. They have shown their potential recently and the best is yet to come.”
Gunners boss Mikel Arteta is confident Zubimendi will reinforce his midfield options after Thomas Partey’s contract expired and Jorginho left the club.
“Martin is a player who will bring a huge amount of quality and football intelligence to our team,” he said.
“He will fit in really well and he has all the attributes to be a key player for us.”
Zubimendi made 236 appearances in all competitions for Sociedad after graduating from the club’s academy and has played 19 times for Spain.
Arsenal finished second in the Premier League last season for the third straight year.
Zubimendi is Arsenal’s second signing of the summer transfer window after goalkeeper Kepa Arrizabalaga joined from Chelsea.
The Gunners are also expected to complete the signing of Christian Norgaard from Brentford. (AFP)