The 19-year-old has been linked with Manchester United and Wigan recently.
“It’s another step forward in my professional career,” said De Gea.
“I’ve spent all my sporting life at Atletico Madrid and for me it’s an honour and a dream to be able to play in the first team having come up through the Rojiblanco youth system.
“Everything is happening very quickly, but my objective is to continue working as I’ve always done,” added De Gea on his club’s website.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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