But the 18-year-old is not expected to be thrust into Thomas Tuchel’s first team squad.
The left-sided defender is instead seen as an option for the development squad.
Derby manager Wayne Rooney revealed on Friday that a fee had been agreed with a Premier League club for the highly-rated teenager.
It has since emerged that Chelsea are the club to have struck a deal.
Rooney said: “We’ve agreed a fee with a Premier League club for Dylan Williams – I couldn’t stand in the way of his opportunity.”
Tuchel is still hoping to bring in at least one addition before the January window closes, with left wing-back the priority position, following Ben Chilwell’s anterior cruciate ligament surgery.
The German had hoped to sign cover before now, warning earlier in the month that his side’s season could be wrecked if they failed to strengthen in the face of a debilitating injury list.
Since then he has seen his title challenge crumble, with Chelsea now 12 points adrift of leaders Manchester City, having won one of their last seven Premier League games.