Making the first move
The Senegalese has become the Black Cats first signing of the summer, securing a four-year contract at the Stadium of Light.
The central defender had only moved to Stamford Bridge last summer, after a move from Nantes.
He only made one appearance from the Blues, and spent the second half of last season on loan at Bundesliga side Werder Bremen and secured their top-flight survival.
Djilobodji told safc.com: "I'm so happy to join Sunderland, I believe we are going to do something this year" and believes "Sunderland Football Club is a big club, a big team, with big fans."
He concluded:"We are going to do our best to give the fans what they deserve" and admitted "the coach (Moyes) called me yesterday and I was so happy, we are going to work to improve."
Moving on from Wearside
Despite finally bringing people into the club, players continue to leave, and added to that list on Friday.
Will Buckley became the latest player to leave Wearside, making a season-long loan move to Championship side Sheffield Wednesday.
The midfielder is expected to make his debut on Sunday, in their opener against Aston Villa, and Buckley shared his delight at moving to Hillsborough.
He told swfc.co.uk: “The club, the manager and what the team achieved last season, it’s the kind of thing you want to be part of" and admitted “as a player, you want to be part of a club that is pushing forward and Sheffield Wednesday certainly fits the bill."
Buckley concluded: “Because it’s a season-long loan, it will help in the settling process and I can take it that this is my club now.”
Sunderland AFC will take on Manchester City at the Etihad Stadium on Saturday, August 5 with kick-off at 5:30pm BST.