The Burkina Faso midfielder played in a Chelsea age group match at Arsenal in October 2011 whilst two years under the right age.
International transfers are only allowed for players over the age of 18.
The Premier League said all rules were followed in Chelsea's signing of Traore on January 1, 2014, the first day of the transfer window opening following his 18th birthday, on September 6, 2013.
A Chelsea spokesman said of the 20-year-old: "Bertrand Traore was registered by Chelsea FC in January 2014 in compliance with FA and Premier League Rules.
"Prior to that date, he was party to an option agreement which enabled the club to acquire his registration in January 2014.
"The option agreement was registered with, and approved by, both The FA and the Premier League."
Traore scored for the Blues against a Malaysia XI in their pre-season tour to Asia in 2013.