The England international completed a £15m move to the defending Premier League champions Chelsea last week.
Barkley has signed a four-and-a-half year deal with the west London side to start a new chapter in his career.
The 24-year-old attacking midfielder has failed to realise his undoubted talent at Goodison Park.
The Liverpudlian talent hasn’t been able to establish himself as a regular in the England team given his poor performances at Everton.
Barkley will work under Antonio Conte at Stamford Bridge, with the Italian coach known as a hard task master.
Former England manager McClaren believes Barkley will improve in a more disciplined role in Conte’s team.
“He has been loose and indisciplined,” McClaren told Sky Sports. “He will get that at Chelsea. It will take him to a different level.”
Chelsea played out a frustrating goalless draw with 10-man Leicester City at Stamford Bridge in the Premier League on Saturday.
Barkley was linked with a move to Chelsea in the summer in a £35m deal but the England star turned down a move at Stamford Bridge.
The England star scored 27 times in 179 games in all competitions during his eight-season spell in the Everton first team.
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