May had been on personal leave from the Demons for several weeks after police were called to his house after a complaint on January 29.
The 34-year-old, who was contracted for the 2026 season, has reportedly reached a confidential settlement with the club.
He announced his retirement on Sunday night via social media and is expected to address Demons players on Monday.
"It's with a heavy heart that I've decided to step away and retire from the AFL," May posted on Instagram.
"It's an incredibly tough decision to make on the eve of the season, but I know it's the right one for myself, my family and the team."
May started his career with Gold Coast in 2011 and captained the Suns before moving to Melbourne at the end of 2018.
The two-time All-Australian played 251 games and was a key figure in the Demons' drought-breaking 2021 premiership.
"As a kid from Darwin, all I ever wanted was to play one game of AFL," he posted.
"To have lived that dream and had the career I've had is something I'll be forever grateful for."
May said Melbourne and new coach Steven King "deserve some clean air and no distractions moving forward" and wished them well.
As recently as last week, Demons captain Max Gawn had been hopeful May would return to the club.
"He's a premiership player and a very, very decent fullback," Gawn told AAP.
"So, yeah, hopefully that all gets worked out at some point."
In a club statement on Sunday night, Melbourne said May had decided to retire in order to "focus on his family and his own personal growth".
Demons CEO Paul Guerra thanked May for his contribution to the club.
"We thank Steven for his efforts in the red and blue and the commitment he brought to the club during his time," Guerra said.
"We're pleased that Steven has made the decision that, at this stage of his life, stepping away from football to focus on building a positive future for himself and his family is his best path forward.
"We wish Steven and his family all the best as he embarks on the next chapter of his life."
Melbourne offered up May for trade last year but could not find a buyer.
His retirement means the Demons can replace him on their list before Monday's supplemental selection period deadline.
May and former Gold Coast teammate Dion Prestia are also fighting charges after a late-2024 brawl in Sorrento on Victoria's Mornington Peninsula.
The pair have asked for the charges to be withdrawn, saying they were not present at the brawl.
Last year, May had a heavily-scrutinised on-field argument with Gawn after the final siren in the King's Birthday loss to Collingwood.
In 2022, May was suspended for one match and apologised after he was involved in a fight with teammate Jake Melksham at a venue in Prahran.
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