The Two And A Half Men star is currently receiving rehab treatment in his Hollywood home.
His hit TV show has been put on an “indefinite” hiatus while he seeks help.
The 45-year-old star was rushed to hospital last Thursday suffering from “abdominal pains”.
Although sources close to Sheen – America's highest-paid television actor – have denied the reports, other sources including porn stars who claimed to be at his home on the night, said Sheen went on a 36-hour drugs binge that resulted in the early-morning dash to hospital.
In a statement to fans, Sheen said: “I have a lot of work to do to be able to return the support I have received from so many people.
“I want to say thank you to my fellow cast members, the crew of Two And A Half Men and everyone at CBS and Warner Bros, especially Les Moonves and Bruce Rosenblum for their concern and support.
“And to my fans, your good wishes have touched me very much. Like Errol Flynn, who had to put down his sword on occasion, I just want to say, thank you.”
Flynn, who died in 1959, aged 50, was as famous for his off-screen antics as his swashbuckling roles in films such as The Adventures Of Robin Hood, Captain Blood and The Sea Hawk.
He had a reputation for his womanising, boozing and brawling. It was a lifestyle that caught up with him in November 1942, when two underage girls, Betty Hansen and Peggy Satterlee, accused him of statutory rape.