The Spaniard has been a standout for AFC Bournemouth this season, after he arrived from the Italian giants on an initial loan move on deadline day in the summer.
As reported, that loan move included an obligation to buy clause that would be triggered if the right back started, or played at least 45 minutes of 50 per cent of games he was available for.
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That clause was triggered as the right back started in the 1-1 draw with Aston Villa on Saturday, with Jimenez also starting for the Cherries in their 2-1 win at Everton on Tuesday night.
The 20-year-old signs a five-year deal with the Dorset club, keeping him on the south coast until 2031.
Bournemouth will pay €19million for the 20-year-old, with €5m in possible add ons, with Milan taking €5m of the upfront fee and half of the remaining money.
Alex Jimenez. goal. (Image: Richard Crease)
The rest of the funds will go to Real Madrid, where Jimenez started his career in the Spanish club’s famed academy.
Madrid did hold buy back clauses in their deal to sell him to Milan, but these are forfeited now Jimenez has completed his move to the Cherries.
Jimenez’s signing means the club have spent more than €450m, which is just under £400m, in the past two and a half years.
The Spaniard has demonstrated his talent since his arrival in England, but also his versatility and adaptability.
Primarily a right back, Jimenez has also been successfully deployed on the right wing at times this term.
In total, he has made 22 league appearances for the Cherries, and one in the FA Cup, scoring one goal and providing one assist.
Alex Jimenez doubled the Cherries' lead with his first goal for the club. (Image: Richard Crease)
He has started 18 in the league, including the past 13 games, notching his first goal for the club last month in the 3-2 victory over Liverpool.
The past two games have seen him play at right back behind new signing Rayan, a hugely exciting right flank for the Cherries of two young players with plenty of potential.
Speaking on the confirmation of Jimenez’s permanent move, AFC Bournemouth’s president of football operations, Tiago Pinto, told afcb.co.uk: “Alex is a young talent, who has already demonstrated his energy and commitment to the squad during these opening months with the club.
“He has incredible pedigree, having begun his development at both Real Madrid and AC Milan. We’re delighted to have him as part of our project, which began last summer and now continues after the obligation was triggered.”