Sheen's thanks come as his off-camera antics, which led to a trip to the hospital last week and a return to rehab, caused a halt of production on television's highest-rated comedy, "Two and a Half Men."
In a four-paragraph statement, Sheen thanked his bosses, CBS chief Les Moonves and Warner Bros.' TV division President Bruce Rosenblum, for "their concern and support."
He did not offer any new details on his treatment. "I have a lot of work to do to be able to return the support I have received from so many people," Sheen's statement said.
It was issued hours after the Los Angeles Fire Department released a 5-minute recording in which Dr. Paul Nassif said he received a call from Sheen's residence and spoke with a secretary who sounded worried about the 45-year-old actor.
"They said don't call 911, but I got (Sheen) on the phone and he was very, very intoxicated, also apparently in a lot of pain," Nassif said.
Sheen was taken to a Los Angeles area hospital last Thursday and was released later that day. Sheen's publicist, Stan Rosenfield, cited the actor's history of hernia problems and later said his client went into rehab, but he did not say why.
Rosenfield declined to comment Wednesday on the actor's condition, citing medical privacy laws.
The statement demonstrated a different tone from the actor, who after his hospitalization sent a text message to an editor of the celebrity website Radaronline.com saying he was fine. "People don't seem to get it.... Guy can't have a great time and do his job also?" the website reported Sheen writing.
In Wednesday's statement, Sheen likened himself to another Hollywood actor who attracted notoriety for his off-camera behavior.
"Like Errol Flynn, who had to put down his sword on occasion, I just want to say, 'thank you.'"
Flynn, the 1930's movie idol famous for his swashbuckling roles, also made headlines for his off-screen personal and legal troubles.
In the 911 call, Nassif is heard asking a dispatcher whether anyone from Sheen's camp had called, and when told that no one had, the doctor said: "These people are afraid to call."
During most of the call, Nassif could be heard finding the address to Sheen's home so Nassif could give it to the dispatcher. Nassif was talking to his wife, Adrienne Maloof-Nassif, a co-star of the reality TV series "The Real Housewives of Beverly Hills," and placed another call to find Sheen's address.
When the dispatcher asked Nassif for further updates, he replied: "All I know is I got a secretary who called and said he's in severe pain and is intoxicated. He said he's very worried but he said don't call anybody."