Chavarria arrives at Stamford Bridge to cover the departure of fellow Spaniard Marc Cucurella, who departed for La Liga giants Real Madrid.
An agreement between Chelsea and Vallecano was reached for a figure close to 23 million euros (£19.6m), including add-ons, as the English side were not willing to pay the 50 million release clause set for the Catalan defender.
"For me, it’s a dream, as Chelsea is one of the most important clubs in the world. It’s a great opportunity, but I’m ready and I’ll work hard to help the team achieve success," said Chavarria in his first comments as a Chelsea player.
"There are many people who have helped me get here and I have to thank my family. They have always supported me and everything I have achieved today has only been possible thanks to them."
The former Rayo player sees his hard work rewarded after a historic 2025/26 season, during which the Vallecanos reached the final of the Conference League.