The club apologised to Johnson earlier this month for the abuse that he suffered as a Blues trainee in the 1970s.
Johnson, 57, revealed that Chelsea paid him £50,000 to keep quiet about allegations against former chief scout Eddie Heath.
A Premier League statement read: "After careful consideration, the board has determined that no Premier League rules were broken by the club not reporting this matter to them in 2014.
"The League has requested that Chelsea agrees to a full safeguarding audit from an independent safeguarding expert.
"The League has no reason to have any concerns about Chelsea's current provisions in this area, but, given the seriousness of these historical allegations, feels that such a review is an appropriate course of action.
"The League has also requested that Chelsea provides them with details of the current review the club has asked an external law firm to undertake into historical abuse and how it handled Mr Johnson's claim, and that a full copy of the review is provided to the Premier League and The FA upon its completion - Chelsea has agreed to these requests."
In an earlier statement, the Stamford Bridge club acknowledged that Johnson had "suffered unacceptably" after joining Chelsea as an 11-year-old in 1970 because of Heath, who died of a heart attack in the 1980s.