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.
Barkley made 150 Premier League appearances for the Merseyside club he joined as an 11-year-old, making his league debut in 2011.
Barkley was close to joining Chelsea in the summer but pulled out at the last minute after deciding to first recover from his long-term injury and then decide upon his future.
However, Barkley said this evening that he was "overwhelmed" by the chance to move to the champions, where he will wear the No 8 shirt.
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Chelsea struggled against the Canaries, for whom Alex Pritchard , Josh Murphy and James Maddison excelled going forwards. When you play in this trophy you know it is very hard , but today the commitment of my players was very good.
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.
"I think that we are resigned and the club was resigned before I got here that we're going to lose Ross and I can't see that changing", said manager Sam Allardyce on Thursday.
Barkley scored five goals and recorded eight assists in the Premier League last season as Everton finished seventh in the table.
Barkley has yet to play this season due to a hamstring injury but he is nearing match fitness. It's a good opportunity for the club to buy this player. He has good prospects for Chelsea. "He is very strong physically and has good technique", Conte added.
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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.
"He had a bad injury and has not played for seven months".
The 24-year-old England worldwide - who has missed the first half of the season through injury - nearly joined Chelsea in the summer transfer window but rejected a Deadline Day move.
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