The 23-year-old, who has been given the number 33 shirt at Stamford Bridge, arrives in England after two-and-a-half fruitful seasons in the Italian capital.
Palmieri began his career in his native Brazil with Santos before joining Serie A side Palermo on loan in 2014 and Roma permanently the following season.
Neither Chelsea nor Roma have disclosed the transfer fee, but Sky Sports News claims that the Blues agreed a deal of £17.6m with the Giallorossi for the Brazilian, plus £7m in add-ons.
"I came here because it's a great team with a great history," Palmieri told the official Chelsea site. "Today I am realising one of my dreams to pull on the shirt of such a great club.
"English football is something I have been watching since I was 15 years old. It is a really beautiful game over here but it is going to be even more beautiful to play it."
Palmieri had been lined up as part of a double swoop with Edin Dzeko, but Chelsea reportedly abandoned a move for the former Manchester City striker due his contract demands.