The 57-year-old waived his right to anonymity earlier this week to reveal that the Blues paid him £50,000 not to go public with the allegations that he was sexually abused by ex-coach Eddie Heath in the 1970s.
Chelsea released a statement on Saturday evening, declaring that a full external review would be launched to explore whether a proper investigation was carried out when Johnson's claims first came to light, while also exploring why it was not reported to both the Football Association and Premier League.
"We are fully committed to ensuring the safety and well-being of all children and young people who are in our care or attending our premises," the statement read. "Their welfare is of paramount importance. We pay tribute to the enormous courage of the people who have spoken out about the horrific abuse which they endured, including former Chelsea player Gary Johnson.
"We recognise that to do so, after carrying the burden of those events for so long, must have been an extremely difficult thing to do. This is a challenge for all clubs and everyone involved in the game. As a club, we are absolutely determined to do the right thing - to fully support those affected, and the investigations being carried out.
"We are working with the Premier League, the Football Association and the police in helping all victims. It is clear that Gary Johnson suffered unacceptably while in our employment in the 1970s for which the club apologises profusely."
Heath, a chief scout at Stamford Bridge for more than a decade until 1979, died before the allegations came to light.