The 36-year-old, who went into hiding after his brief arrest last week following a family bust-up, released a statement thanking "mum and dad for helping me through the toughest week of my life".
"I know I have some mental health issues and I am seeking help here in Australia and I will be also going overseas," he said in the statement released late on Tuesday.
In 2014, he checked into a US rehabilitation clinic to treat an addiction to sleeping pills.
Hackett's father Neville had reported the former 1 500m world record-holder missing, sparking fears for his safety.
The retired swimmer posted a picture on social media showing himself with a black eye, and accused his brother Craig of beating him up.
But Hackett said in the statement he had resolved those differences.
"My brother and I have reconnected and love each other very much - our family has always been our priority," he said.
Police released the double Olympic gold medallist last Wednesday without charge just hours after his family had him arrested following a bout of heavy drinking which led to "uncontrollable rage".
