Barkley cited his own injury as the reason for the change of mind back then - he hasn't played all season in fact, after undergoing surgery in July - though it seemed like that he really wanted to join Spurs instead.
Barkley was on the verge of becoming a Chelsea player in the summer transfer window.
Speaking to Chelsea's website about his 14th signing since taking over the reins of the west London club in 2016, Conte expressed his excitement at Barkley's ability to become an ever better player at Stamford Bridge.
Spurs have been long time admirers of the Everton man, but it now looks like they will miss out on the enigmatic 24-year-old.
Barkley scored five goals and recorded eight assists in the Premier League last season as Everton finished seventh in the table.
The 22-capped England worldwide has not played a single game for the Toffees this season, and has always been prone to injury throughout his career, along with being an inconsistent performer for the Merseyside outfit.More news: Captain Marvel Adds She's Gotta Have It Star
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Chelsea have completed the £15m signing of Ross Barkley from Everton. He can have good prospects for Chelsea. "He is very strong physically and has good technique", Conte added.
Conte urged caution over expectations for Barkley. I think the club decided on this investment also for his contract.
"I think it's a great move for Chelsea and I think it's a great move for him", he told Sky Sports show The Debate.
"He's a good prospect but it's very important to understand when he can recover from his injury". 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.
"We have to hope to recover him very quickly and have him for the rest of the season".