Defending champions Chelsea had agreed a £35m fee with the Toffees last August but the move fell apart.
"I'm overwhelmed, I'm looking forward to it and I'm really excited to get started", Barkley told Chelsea's website.
It is as a result of that hamstring problem that the 24-year-old England global has not played a single minute of football so far in 2017/18.
"We have to look at what we bring in, what we can improve the side with and try to move on and make as many league points as we possibly can between now and the end of the season".
Barkley has yet to play this season due to a hamstring injury but he is nearing match fitness.
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He said: 'For sure we're talking about a young player, an English player. He's a good prospect. I think the club decided on this investment also for his contract. "He is very strong physically and has good technique", Conte added.
"But I think for Ross at the moment he's got to get fit".
Conte had expressed his opinion to the Chelsea hierarchy and left them to do the negotiationsm but has been a big fan of Barkley for a long time.
This is not necessarily a bad thing for Tottenham, however, what with Barkley's less than impressive injury record, and his inconsistent form over the past couple of years.
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.
The England global sealed a £15m transfer to Chelsea to become Antonio Conte's first signing of the January transfer window.