The South Australia-born Pickett had been a trade target of Port Adelaide, where his uncle Byron Pickett played 55 of his 204 AFL games.
But Pickett has opted to remain at Melbourne in a deal lasting until the end of the 2027 season.
"The club has embraced me and my family and I can't thank them enough for their support," Pickett said in a statement on Monday.
"Everything I do is to make my family proud and the respect and understanding my teammates and coaches have shown us means a lot."
Pickett's signature had been coveted by the Demons, who drafted the brilliant forward-midfielder with pick 12 in 2019.
"We are obviously thrilled that Kozzy has agreed to terms," Melbourne's list manager Tim Lamb said.
"At just 21 years old, he has already proven himself to be one of the premier small forwards in the competition, kicking 40 goals in each of the last two years.
"Everyone has now seen his ability around the ball and he is just scratching the surface in terms of where he can take his game."
Lamb described Pickett's rapid development as testament to the 67-gamer and his coach Simon Goodwin.
"Koz is universally loved within the club and has a great relationship with Goody and his teammates," Lamb said.
"He brings joy to everyone with his infectious and caring personality and is a critical cog of both our current and future ambitions."
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