Hackett, who won 1,500 metres freestyle gold at the 2000 and 2004 Olympics, created headlines Down Under this week after being found topless and disoriented at Melbourne's Crown Casino early on Saturday morning.
"Grant is currently in transit to seek treatment for a dependency to Stilnox medication," his manager Chris White told News Ltd media.
"His family and friends are enormously proud of his courage in pursuing this course of action."
Hackett publicly admitted to a dependency to Stilnox in the lead-up to the 2012 London Games, prompting the Australian Olympic Committee to ban athletes from using it.
The 33-year-old touched down in Los Angeles on Tuesday but denied he was entering a rehabilitation clinic.
"No, not as such ... I'm just going away for a break and looking forward to enjoying myself," he told reporters at the airport.
"It's a bit of an exaggeration ... I'm not calling this rehab whatsoever. This is a retreat to get away for a while, to recharge the batteries which I've been planning for some time."
Hackett's father said his son was in "a little bit of denial."
"He thinks he just needs a bit of a recharge and a rest," Neville Hackett told local radio station Triple M.
"I'd say rehab is certainly something that's needed there."
Hackett's flight follows the troubles of another Australian swimming great Ian Thorpe, who checked into a health clinic earlier this month to seek treatment for depression.
The five-times Olympic champion, widely regarded Australia's finest swimmer, had been taking anti-depressants and medication for a shoulder injury.
Hackett, who has worked as a television pundit and for a local bank since retiring from swimming after the 2008 Beijing Games, was photographed shirtless in the lobby of Crown Casino where he was staying at a friend's apartment.
He told local media he had rushed out of the apartment to look for his four-year-old son after waking up to find him missing.
Though Stilnox was banned for Australian Olympians, members of the country's 4x100m men's freestyle team took the sedative as part of an unofficial "bonding" exercise in the lead-up to London and were later fined after an investigation.
- Sports & Recreation
- Australian Olympic Committee