The 31-year-old Senegal captain becomes the second signing after Manchester City striker Raheem Sterling since Todd Boehly’s consortium bought the club.
“I’m very happy to be here with this team at Chelsea,” said Koulibaly.
“It’s a big team in the world and my dream was always to play in the Premier League. Chelsea came first to get me in 2016 but we didn’t make it. Now when they came to me I accepted it because they really wanted me to come to the Premier League to play for them.
“When I spoke to my good friends Edou (Mendy) and Jorginho they made my choice easier.”
Koulibaly, who led Senegal to the African Cup of Nations title earlier this year, joined Napoli from Genk in 2014 and made 317 appearances for the Italian side. He won the Italian Cup title in 2020.
His arrival at Stamford Bridge follows the departures of defenders Antonio Rudiger to Real Madrid and Andreas Christensen to Barcelona, both on free transfers.
“Koulibaly is a natural leader and a strong character,” Chelsea said in a statement.
“He has plenty of experience challenging for domestic and international titles and joins the Blues ahead of the 2022/23 campaign aiming to do just that.”