The England Under-20s coach has reportedly beaten competition from former Southampton manager Nathan Jones and ex-Rangers boss Michael Beale.
Edwards will replace Gary Rowett, who was sacked last month.
He is understood to be keen to bring staff from Chelsea's academy, including Myers who managed the Under-21s last season before moving into the loan department.
Chelsea have yet to release Myers as talks go on. They are braced for further approaches for other academy staff.
Edwards learned his trade in Chelsea's academy, before becoming Frank Lampard's assistant at Derby County.
He returned to Chelsea to coach in the first team when Lampard was appointed manager and then followed him to Everton.
Edwards has been working in an interim role with England's Under-20s since the October international break after leaving Chelsea for a third time after Lampard's interim spell last season.