Cole, who was 27, had been forced to retire as a professional player in February last year owing to a heart attack.
Writing on their official twitter feed, the League said: "We are sad to hear former Southend, Stevenage and Oxford player Mitchell Cole has passed away. Our thoughts are with his family and friends."
Cole, who was married to the sister of England international Joe Cole, scored for Stevenage against Kidderminster at Wembley in the 2007 FA Trophy Final. He said last year he would be risking death if he were to play again.
In an interview with The Sun he said: "A few players around the world die of this every year. The specialists told me that every day I have a one percent chance of dropping dead and sport quadruples that risk.
"When he gave me the numbers and showed me images of my heart, it hit me hard."
Despite retiring from the professional game last year, Cole did make a handful of non-league appearances, some of which came for Arlesey Town.
However, according to their director of football, Gary King, watching Bolton midfielder Fabrice Muamba suffer a cardiac arrest in an FA Cup tie with Tottenham in March convinced Cole to give up the game for good.
King told journalists: "We were watching that game in the clubhouse and he turned to me and said `I`m not playing again`, although I`m told he might have been playing five-a-side in London last night."
The PFA joined the Football League in expressing their condolences, tweeting: "The PFA is deeply saddened by the loss of 27-year-old Mitchell Cole, our thoughts are with his friends and family."
Cole's former clubs were among the first to pay tribute, with West Ham posting on their official Twitter feed: "Everyone at West Ham United has been saddened to learn of the death of former Hammers Academy player Mitchell Cole at the age of 27. RIP."
Stevenage added on their official account: "The club are saddened to hear of the passing of former player Mitchell Cole. Our thoughts are with his family at this time."
Southend United said they were "extremely saddened" to hear the news, while Oxford United tweeted: "Our thoughts are with the family of Mitchell Cole."