The 35-year-old, who had previously overcome testicular cancer, was diagnosed with lung cancer in May, causing him to miss the start of the 2014-15 season while he received treatment.
Carter made his return to snooker at the General Cup in Hong Kong in October, beating Shaun Murphy in the final to emerge victorious.
The three-time ranking event winner then exited at the first-round stage of the UK Championship in York earlier this month, but took to Twitter on Friday to share news of his recovery.
"Two beautiful words that I've been waiting for!! 'ALL CLEAR' I can now concentrate on getting my life and career back! #beatingcancer," he wrote.
Carter, who also has Crohn's disease, was on the receiving end of a 5-4 defeat to Sam Baird on Thursday in qualifying for the German Masters - a tournament he won in 2013.