"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."
The versatile Dutch defender, who can play in the centre of defence or at right-back, had been linked with Manchester United, while Bayern Munich were also known to be interested.
He has won 15 caps for the Netherlands, including four at the Qatar World Cup, where he helped Louis van Gaal's side reach the quarter-finals.
Timber said he has "always been a fan of Arsenal", which stemmed from his brothers' love for the club.
"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," said Timber.
"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."
He will add strength to the spine of an Arsenal team that finished runners-up to Manchester City in a closely fought Premier League title race last season and qualified for the Champions League after a six-year absence.
His signing follows that of 24-year-old Germany forward Kai Havertz from Chelsea, with West Ham midfielder Declan Rice also close to completing a club-record 105m move to Emirates Stadium.
Arsenal have also agreed new contracts with Bukayo Saka, 21, and Reiss Nelson, 23, while experienced Switzerland midfielder Granit Xhaka, 30, joined German side Bayer Leverkusen for 21.4m.
Timber made 47 appearances in all competitions for Ajax last season, including all six of their games in the Champions League group stage, and helped the Amsterdam side to win the Eredivisie title in 2021 and 2022.
Arsenal sporting director Edu said: "We are very happy to bring Jurrien to Arsenal. He is a player that we have admired for a long time, so it's a credit to everyone in our team that made this happen.
"Jurrien is a young, talented international player, who fits our vision of competing with a young, strong squad. I know Jurrien cannot wait to get started and we're really hoping that he will be a great success here for many years."
'Timber reminiscent of Van Dijk' - Analysis
Arthur Renard, Dutch football journalist
Defensively solid all round, a great ability to read the game and very strong on the ball, it is understandable why Mikel Arteta was keen to bring Timber to the Emirates.
For the national team he has played mostly on the right of a three-man defence, next to Virgil van Dijk. The Liverpool centre-back praised Timber's development, saying he was not nearly as far along at the same age, describing him as a great player and true professional.
In some ways Timber's game is reminiscent of Van Dijk's - both are calm in one-on-one situations, anticipating strikers' movements and choosing the right moment to intervene.
Their reading of the game makes them stand out, as well as being able to receive the ball in pressured situations.
Timber's impressive technique and ball control come in handy when going forward, but his defensive characteristics are equally impressive as he uses his body well to hold players off, which is also demonstrated by his well-timed blocks and sliding tackles.
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