All three players have agreed to new two-year deals, keeping them at Alberton until the end of the 2023 season.
Georgiades made his debut for the club in Round 1 this year and went on to play seven games for the season.
The 19-year-old proved to show plenty of potential as a key forward for the Power, demonstrating strong skills in the air and by foot.
Bergman was taken with the 14ht overall selection in the 2019 draft and was an emergency for Ken Hinkley’s side on several occasions this season.
Williams’ 2020 season was riddled with injuries after forward sustained a groin injury, restricting his time on the training track this year.
Port Adelaide general manager of football Chris Davies stated his excitement to have the trio sign-on for the future.
“I think a lot of our supporters will be excited by what they saw from Mitch in the games he played at AFL level in 2020,” he said.
“His running capacity and ability to take strong marks in front of goal were a real highlight and we know there is still plenty of upside in his game.
“Both Miles and Dylan have settled well in Adelaide and have become popular members of our playing group.
“Unfortunately given the restrictions placed on our club’s participation in the SANFL competition, our people would not have had much chance to see the boys in action but that did not stop them working hard on the track and making the most of their limited match simulation opportunities.
“We think Miles, Mitch and Dylan will each have a long future with the Port Adelaide Football Club and we look forward to their continued improvement over the coming seasons.”