Yze has won the Tigers job after a series of recent interviews, beating out caretaker coach Andrew McQualter.
After Hardwick abruptly quit as Richmond coach in May after 13-and-a-half seasons, McQualter led the Tigers to seven wins from his 13 games in charge.
Yze has been an assistant in the AFL system for more than a decade, first working part-time under Alastair Clarkson back at Hawthorn in 2012.
Richmond confirmed the news on Thursday night, on Yze's 46th birthday.
"We have no doubt that Adem is the right man to lead us into the future," Richmond president John O'Rourke said.
"Adem brings an enormous breadth of experience to the club.
"He has a deep understanding of the game and what drives on-field success from a strategic and cultural perspective.
"Adem has great energy and is highly competitive, and during the appointment process, it became increasingly obvious that he was a great fit for our club.
"He was the ideal candidate, and we have no doubt our playing group will thrive under his coaching."
After six full-time seasons with the Hawks, Yze moved to the Demons, the club he played 271 games for, ahead of the 2021 season.
He played a crucial role with head coach Simon Goodwin in Melbourne's charge to the 2021 premiership, the Demons' first flag in 57 years.
It ends a long wait for Yze to land a senior job, having previously interviewed at Adelaide, GWS and Essendon.
He twice missed out last year, vying for the Giants and Bombers positions eventually won by Adam Kingsley and Brad Scott, respectively.
"This is a club steeped in history and blessed with a magnificent supporter base. I feel very humbled to have been given this opportunity," Yze said.
"I can't wait to meet the playing group and start building towards the 2024 season."
Hardwick was last month named Gold Coast's new coach following the axing of Stuart Dew in July.
O'Rourke thanked all those who had taken part in the coaching process.
"Andrew took the selfless decision to take on the interim role when Damien Hardwick left the club, and he has handled himself with confidence and class," he said.
"He continued to impress during the interview process, and I have no doubt he will be a future AFL coach."
Yze will front his first press conference as Richmond coach on Friday at Punt Rd.
The Tigers will attempt to bounce back from a 13th-place finish this year without premiership stars Trent Cotchin and Jack Riewoldt, who retired at season's end.
Melbourne thanked Yze for his contribution to the Demons and wished him well at Richmond.
"Adem has had a significant impact on our football program since joining the club three years ago," Demons football performance boss Alan Richardson said.
"His ability to read the game and the direction he was able to provide our players and coaches was first class, and we are thrilled to see him get this opportunity."
ADEM YZE
Age: 46
Playing career: 271 games for Melbourne (1995-2008) and 234 goals
Coaching career: Hawthorn 2012-2020 and Melbourne 2021-23.
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