David Limbaugh made the announcement to Internet personality Matt Drudge, who was sitting in Wednesday for the conservative commentator.
Limbaugh left the air Oct. 10 after acknowledging that he had been abusing prescription painkillers.
Limbaugh plans to resume his regular schedule, hosting his three-hour show on weekdays for his audience of 20 million, his brother said.
"He's obviously champing at the bit to get back to doing what he does best," David Limbaugh said.
Rush Limbaugh said last month that he was checking himself into a treatment center to "once and for all break the hold this highly addictive medication has on me."
His brother said the host successfully completed the first phase of his treatment. He did not say what the next step is.
Limbaugh's admission to drug addiction came several days after the National Enquirer ran a story that quoted his maid as saying she was his drug connection. She said Limbaugh had abused OxyContin and other drugs.
A law enforcement source in Palm Beach County, where Limbaugh owns a $24 million oceanfront mansion, said Wednesday that an investigation into Limbaugh's drug use by the state attorney's office continues.
Limbaugh said last month he had been asked to "limit my public comments until this investigation is complete." His attorney, Roy Black, would not comment Wednesday on the investigation.
Limbaugh's drug admission came less than two weeks after he quit as a pro football commentator with ESPN. He left after creating a furor by saying that he believed the Philadelphia Eagles' Donovan McNabb was overrated because the media wanted to see a black quarterback succeed.