Timber has signed a five-year contract at the Emirates Stadium to become Arsenal's second summer signing after Kai Havertz.
The 22-year-old made 121 appearances for Ajax after breaking into the club's first team in March 2020.
He won two Eredivisie titles and one KNVB Cup with Ajax.
Timber has won 15 caps for the Netherlands national team and played four times at the 2022 FIFA World Cup in Qatar.
Timber has been handed the number 12 jersey at his new club.
Timber told the club's website: "I've always been a fan of Arsenal. It was because of my brothers. They were always Arsenal fans, and I just loved seeing Arsenal play. They had big players, the way they played, the style. I just love the club.
"I had this from a young age, but my brothers kind of put that in me. I liked watching Robin van Persie of course, and Thierry Henry. They were my favourite players."
Arsenal manager Mikel Arteta added: "We're really excited that Jurrien has joined us. He is a versatile young defender, who will fit into our system and provide our squad with so much added quality.
"Jurrien is a young player, but has already achieved so much. He has experienced what it's like to go to a major international tournament on more than one occasion, as well as the trophies he has won with Ajax. We look forward to welcoming and integrating Jurrien into the squad."
