Arsenal sign Spain midfielder Zubimendi
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," said the defensive midfielder, who is understood to have put pen to paper on a five-year deal.
"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."
The Athletic reported that Arsenal paid above Zubimendi's 60 million euro ($71 million, £51 million) buyout clause in order to spread the cost of the fee over a number of installments.
Zubimendi, 26, made 236 appearances in all competitions for Sociedad after graduating from the club's academy and has played 19 times for Spain.
He will reinforce manager Mikel Arteta's midfield options after the departures of Thomas Partey and Jorginho.
Zubimendi's arrival paves the way for Arsenal's record signing Declan Rice to play a more attacking midfield role alongside captain Martin Odegaard.
"Martin is a player who will bring a huge amount of quality and football intelligence to our team," said Arteta.
"He will fit in really well and he has all the attributes to be a key player for us."
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 midfielder Christian Norgaard from Brentford.
Arsenal finished second in the Premier League last season for a third straight year and reached the semi-finals of the Champions League but ultimately ended up without a trophy for a fifth consecutive season.
Attention will now turn to the forward line as the Gunners try to see off champions Liverpool and Manchester City and claim a first league title since 2003/04.
Arteta's men had to cope without a natural striker for much of last season due to long-term injuries to Kai Havertz and Gabriel Jesus.
Reports on Sunday suggest a deal for Sporting Lisbon striker Viktor Gyokeres is on the verge of being sealed to fill the need for a new number nine.
Arsenal have also been linked with a move for Chelsea's Noni Madueke.