The 24-year-old has signed a four-year contract and joins the Spanish fee for a fee believed to be around €7million.
“I wanted to sign for one of the best club’s in Europe,” he told their official website.
“I’m happy to be a part of this club.”
Alderweireld has also been linked with the likes of Bayer Leverkusen and Liverpool this summer.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.