The 34-year-old Hackett, a two-time Olympic gold medallist in the 1,500 metres freestyle, qualified for Australia's 200 metres freestyle relay team at the national championships last week, only six months after announcing his return to training.
Hackett's comeback has been warmly welcomed by an Australian public that was disappointed by the national team's underwhelming performance at the London Olympics.
In qualifying for the 200m relay team, Hackett shaved seconds off his personal best and also smashed his fastest time in the 400 freestyle when narrowly missing out on a second berth at Kazan.
"It gave me a sense of deja vu," Cotterell, who coached Hackett to gold at the 2000 Sydney Olympics and Athens in 2004, told Australian Associated Press. "Nothing has really changed, he's just a more mature version.
"He has champion attributes you can't buy, and that's the make-up of the bloke."
Hackett, who also won silver in the 1,500 at Beijing, returned to the pool after a highly public battle with his addiction to a prescription sleeping medication.
Though a popular and wealthy celebrity in sports-mad Australia, Hackett struggled with life after competition and endured a messy break-up from his marriage to a local singer.
After spending time in rehab in the United States last year, photographs of a lean and muscular Hackett training began appearing in local tabloids before he announced his comeback as simply a "fun" pursuit.
Cotterell said the hard work would now begin in earnest for his protege.
"He's already come further than he ever expected -- now it's more of a mental challenge," Cotterell said.
"He is at a great level already but gains won't come quick, but we know that."
Australia shook up its swimming establishment in the wake of the London Games, where the team slumped to its lowest medal haul in 20 years and were rocked by allegations of bullying, excessive drinking and prescription drug abuse.
With the team building nicely for the Rio Games, Cotterell said Hackett could only prove to be an inspiring presence for junior team mates at Kazan.
"He will add maturity to the team and strengthen the overall culture of it," he said.
"I have been on the team 30 years and he was the greatest team captain."
(Writing by Ian Ransom; Editing by Greg Stutchbury)
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