As a result of the injury, Barkley has not featured for the Toffees this season, so it could take him some time to get up to speed with his new side.
The England global nearly joined the Premier League champions in the summer, only for the transfer to collapse at the last minute.
A repeat of Tottenham, who have also been heavily linked with Barkley, snatching Fernando Llorente at the last minute is not an option.
Speaking about his move, Barkley told the club's official website: "I'm overwhelmed, I'm looking forward to it and I'm really excited to get started".
"To be given a fresh start at a new club like Chelsea, it's unbelievable for..."
"I think with Kante there, Fabregas and Barkley being the runner and joining in, scoring goals from midfield, they'll be a real threat and a good midfield three".
The 24-year-old has not featured for Everton this season due to injury, but has returned to training with the first team.
Conte is desperate to reinforce a squad that has left him 16 points behind Manchester City in the Premier League.
"For sure we're talking about a young player, an English player", said Conte. He's very strong physically, good technique. He has good prospects for Chelsea.
"I think sometimes when you are at your home club, you can be there too long and you have to learn the different levels of the game". He's a good prospect but at the same time, it will be very important to understand when he can recover from his injury.
Ruben Loftus-Cheek is now prospering on his season-long loan at Crystal Palace and fans desperately want him to see him in the Chelsea squad next season.
Chelsea have confirmed the signing of England midfielder Ross Barkley from Everton. Barkley is in the final six-months of his contract at Everton and will thus leave on the cheap with Everton deciding to cash in rather than losing the player in the summer for nothing.