Hooper will miss two Tests against the Pumas after he announced he wasn't in the right mindset to lead or represent the country and would instead fly home.
A mainstay of the national team for the past decade playing 121 Tests, flanker Hooper had been captain a record 68 times and appeared an indefatigable figure through the sport's lows.
Rennie said there was no inkling of Hooper's personal struggle as they prepared for the Mendoza Test on Sunday morning (AEST) until the 30-year-old sought help from the Wallabies team doctor Sharron Flahive, who put the wheels in motion for his return home.
He will travel back to Sydney with his Waratahs teammate Dave Porecki, who is unavailable for both Tests due to a training head knock.
Rennie said it was a courageous decision by father-of-one Hooper, normally a very private character, to admit he needed help.
"Nothing that was evident to us in how he trained - how he contributed around the team, around leadership was excellent - but clearly he's been struggling a bit and masking that pretty well," Rennie told reporters from Argentina on Saturday (AEST).
"Obviously he's been able to suppress things over the past handful of weeks and so we certainly weren't aware of anything but he's such a professional and he was able to get on and do the job.
"He addressed the team today which took an enormous amount of courage to let them know that he's not OK and that he felt it was best for himself and for the team that he gets home.
"It was an easy decision to let him go home where he will get plenty of support around him."
Fellow Test centurion James Slipper will captain the side, while Fraser McReight will replace Hooper in the No.7 jersey to earn his third Test cap.
Rennie said that McReight was match-ready after recently playing in the Australia A Pacific Cup series.
"He's had three 80-minute performances so conditioning-wise it's not an issue," Rennie said.
"They use the same structures as us and he has been in our group in the past and so he'll fit seamlessly."
Hooper skippered Australia during their recent series loss to England which raised some questions about whether he was still the best man to lead the Wallabies.
Assistant coach Scott Wisemantel said at the time that Hooper was "adored" by his teammates.
"You look at his position, how other teams rate him, he's world-class," Wismantel said.
"He's a strong leader. He's a great listener."
Retired cross-code star Karmichael Hunt said his former teammate was in the top five greatest players across the three football codes he played.
"His courage, toughness, dependability and care for this mates is what stands out above all ... wishing him nothing but the best," Hunt tweeted.
The Wallabies, who have a World Cup in France next year, return to Australia for Rugby Championship Tests against South Africa and New Zealand beginning later this month.
Rennie said Hooper hadn't given any indication regarding his playing future and they didn't have a timeline for a return to action.
He praised his player for being a role model for men.
"It's not uncommon in life, is it? It's a cross-section of society and often men will say bugger all and suffer in silence so it took a lot of courage to address the group," Rennie said.
"He has a huge amount of respect from everyone and we want to get him home and get him as much support as we can."
