The German side agreed a deal with Chelsea worth £16.4 million for the 20-year-old defender, per Sky Sports.
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The Spaniard joined the Blues just two seasons ago from Barcelona for £5 million, and have included a sell-on clause in the deal with RB Leipzig.
A statement from Chelsea read: "Marc Guiu has completed a permanent transfer to Bundesliga side RB Leipzig.
"Everyone at Chelsea would like to thank Marc for his efforts during his time at the club and wish him every success as he begins the next chapter of his career with RB Leipzig."