Kay worked as a mentor to former Arsenal and England captain Adams and fellow footballers Joey Barton, Paul Gascoigne and Paul Merson among others.
Adams said: "Peter was my friend as well as a professional colleague and I am saddened by this news.
"He played a major role in changing perceptions and lives, along with helping the charity become what it is today."
Kay helped Adams found Sporting Chance 13 years ago and worked as chief executive until 18 months ago when he stepped down due to illness.
A statement from Sporting Chance said: "Peter was an energetic and inspirational chief executive, who, with Tony, helped change for the better attitudes in sport towards sportsmen and women with addictive illnesses and emotional issues.
"As a result of Peter's work, there are now many sporting figures, current and retired, who are in good recovery, enjoying fine careers and living life well.
"He left a great example for us, one that we will endeavour to follow."
Professional Footballers' Association chief executive Gordon Taylor said Kay's death had rocked the players' union.
He told Press Association Sport: "We at the PFA are all shocked and devastated to hear the tragic news of the death of Peter Kay.
Source: PA
Source: PA