Koulibaly 31, left Napoli after over 8 years at the Serie A club amassing experience across all competitions.
He is regarded as one of the most complete defenders of this generation with his well-built, technically and aggressive style of play.
The transfer cost Chelsea in the region of £33m with potential add-ons included.
He has signed a four-year contract worth around £160,000 per week (£8.2m a year) net plus bonuses to move to Stamford Bridge.
On the International scene, Koulibaly has over 62 caps for Senegal and is also part of the team that won the Africa Cup of Nations 2021.
He flew out to Las Vegas on Friday to join up with his new teammates on their pre-season tour of the USA.
"I'm very happy to be here with this team at Chelsea," Koulibaly said in a statement. "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."
Chelsea will now have Koulibaly, Thiago Silva, Trevoh Chalobah and Malang Sarr as the only senior centre-backs in Thomas Tuchel's squad.
They are still in the race to sign Nathan Ake or Jules Kounde, although the French man has an agreement with Barcelona -- just a matter of agreement with Sevilla is keeping the deal uncompleted.
Koulibaly while in Napoli, made over 300 appearances for the Serie A club since joining from Belgian side Genk eight years ago, being named in the Serie A team of the year on four occasions, as well as being named the best defender in Italy in 2019.