The 52-year-old revealed his illness last month, but an early diagnosis meant it was operable and Sheedy is now recovering at home.
He told Everton's website, www.evertonfc.com: "I would strongly urge anybody who has concerns to go immediately to their GP. My life has been saved through early detection and I am told that over 90% who are diagnosed at the earliest stage are successfully treated. Don't be embarrassed to go otherwise you could die of that embarrassment."
Everton confirmed Sheedy will not require further treatment, but the man who scored against England at the 1990 World Cup said: "I will need regular checks to monitor my recovery."
Sheedy, a cultured left-footed player and a free-kick expert, was a key member of the Everton team that won two league titles in the 1980s. He also had playing spells at Hereford, Liverpool, Newcastle and Blackpool.
He is now working as a coach of the Everton under-18s team, and said: "I would like to say a massive thank you to everybody who sent me messages of support, which I got from all over the world.
"It was very touching and really helped me to deal with my situation knowing that so many people were rooting for me.
"It would be impossible for me to personally reply to everybody but I would like to make special mention of my surgeon Mr Skaife, all of his staff and the staff on Ward 4 at Aintree Hospital who gave me the best treatment and support that I could ever have wished for."
Source: PA
Source: PA