The deal could be completed in the coming days, with the BBC claiming he will have a medical at Stamford Bridge today (Friday) ahead of a £15 million transfer.
The Blues tried to bring the England global to Stamford Bridge in the summer but he opted against a switch on deadline day.
While the Evertonian has been out injured for first half of the season, he has resumed training and thus will be available to play in all four competitions for the Blues.
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The England worldwide is believed to be in London to negotiate terms with the reigning Premier League champions, despite having turned them down last summer.
But they hesitated for too long, hoping to sign him for free in the summer, allowing Chelsea to move into pole position to sign the highly-rated English midfielder.
Some of the Everton fans who were disappointed in his decision not to sign a new contract past year will likely be happy to see him leave.
It will mean the player is leaving Goodison Park after 13 years, having joined Everton as an 11-year-old in 2005.