The two-time World Snooker Championship runner-up was struck with the illness a year after recovering from testicular cancer.
The 35-year-old stepped away from the sport to focus on his health, but has now expressed his desire to return.
Carter wrote on Twitter: "Hi people, not been on here much, been busy getting myself better! I have now finished my chemotherapy and things are really positive!
"I'm feeling much better and it won't be long till I'm back playing again!! Missed it big time..#perspective #beatingcancer."
Carter has won the 2009 Welsh Open, 2010 Shanghai Masters and 2013 German Masters in his career so far.