The 20-year-old, considered one of Europe's brightest young talents, made 34 appearances for the Serie A side since joining from Real Madrid's academy in 2023.
Jimenez spent a decade at Real Madrid's famed youth system, developing from 2012 to 2022, before making the step into senior football.
Jimenez has represented Spain at under-15, under-17 and under-19 levels, and is set to join the under-21 squad during the upcoming international break.
Speaking on the club website, Bournemouth's president of football operations, Tiago Pinto, said: "Alex is a highly regarded young player who has already shown great promise at AC Milan. We are delighted to bring a player with such talent into the club and we believe he will be a strong addition to our squad.
"We're looking forward to working with him once he returns from international duty with Spain."
The defender also expressed his excitement: "I'm very happy. I'm excited about this project and that they've welcomed me so well. I can't wait to start training with the team and playing with the team.
"It has always been one of my dreams to play in the Premier League and as long as I can fulfil a dream, I will be happy."
Jimenez becomes the latest summer recruit for Bournemouth, joining Adrien Truffert, Dorde Petrovic, Bafode Diakite, Ben Gannon-Doak and Amine Adli.
Junior Kroupi is also preparing for his first full season with the squad, giving head coach Andoni Iraola a wider pool of options as the Premier League campaign intensifies.
Arsenal produced a stunning second-half performance to thrash Atletico Madrid 4-0 at the Emirates Stadium, securing a commanding victory in the UEFA Champions League on Tuesday night.
Manchester City ended their five-match winless run away from home in the UEFA Champions League with a commanding 2-0 victory over Villarreal, becoming the first side to win at the Estadio de la Ceramica since Real Madrid in March.
Chelsea have grappled with a disciplinary headache lately, collecting five red cards across their past six outings in all competitions, a tally that includes head coach Enzo Maresca's own dismissal.
Eddie Howe has urged Newcastle United supporters to recreate another "electric atmosphere" at St James' Park as the Magpies prepare to face Benfica in the Champions League on Tuesday night.
