Washington has signed a seven-year contract at Stamford Bridge with the option for a further year.
The 18-year-old played 16 times for the Santos senior team after coming through the youth ranks and scored two goals.
Upon signing, Washington said: "I'm very happy to be joining a huge team like Chelsea.
"I can't wait to make my debut here at such a big club with loads of goals and assists."
It remains to be seen whether Washington will be sent on loan or retained to compete for a spot in the Chelsea attack.
Chelsea are winless in their opening two Premier League games this season and host newly promoted Luton Town on Friday.
