Cole 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 - the first competitive game at the new Wembley. 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 Press Association Sport: "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 had tweeted on Friday night about playing football. On @mitchcole21 he wrote: "London tonight for the usual kick about with the lads!"
Cole suffered from hypertrophic cardiomyopathy which is an irregular thickness of the heart in certain areas.
After being released by West Ham he went on to carve out a carer in the lower leagues after establishing himself at Stevenage.