The 52-year-old, who was diagnosed with the disease in August, underwent successful surgery last month.
"I started back on Monday and I am just easing my way back into it," he told the club's official television channel.
"It's great to be back, it's like I'm starting again at a new club. I had what I had and I've overcome it and I am just really looking forward to being back where I love being and coaching the players.
"It has been a bit of a torrid time. It's a bit surreal - it happened so quickly, I had the operation quickly and I've recovered quickly. It just seems as if it hasn't happened."
Sheedy won two league titles, the FA Cup and European Cup Winners' Cup during a decade-long playing career at Goodison Park.