The NextGen Finals winner stunned the world number three, who is 17 years his senior, 6-7 (11-13), 7-6 (7/3), 7-5, 7-6 (7/5) on Rod Laver Arena.
"That moment is definitely something that I will never, ever, ever forget," said Tsitsipas.
"This match point is going to stay, I'm pretty much sure, forever, for the rest of my life.
"Roger is a legend of our sport. I have so much respect for him. It's a dream come true, my idol became my rival today."
Tsitsipas, seeded 14, became the first Greek in history to reach the quarter-finals of a Slam
"There's nothing really I can say to describe this," added the 20-year-old, bursting with emotion. "I'm the happiest man on earth right now."
The pair's only previous meeting in the mixed team Hopman Cup earlier this month was also tight affair that went to two tiebreaks.
Federer prevailed that day but was at a loss to explain how he created 12 points to break the powerful Tsitsipas serve over four sets on Rod Laver Arena and converted none.
"It definitely didn't go the way I was hoping on the break points," a despondent Federer told reporters immediately after his hopes of winning a record seventh Australian Open were shattered.
- ' Something is wrong' -
"I also didn't break him at the Hopman Cup, so clearly something is wrong how I return him, what I'm trying to do.
"He's doing a good job to defend them."
Tsitsipas said he just tried to stay confident and keep to his game plan under as Federer ramped up the pressure.
"I think I was just very aggressive from the very beginning from his return," Tsitsipas said. "I managed to not make any mistakes, stay in the point, make him play."
The first set tiebreaker was an epic tussle that ended unfortunately when a fan jumped the gun and shouted "out" on a Tsitsipas forehand causing the Greek to miss his next shot.
The second set also went to a tiebreak but this time Tsitsipas quickly took two points against Federer's serve to level the match.
At 4-5 in the third, Tsitsipas forced his first two break points which Federer saved. But he could not repeat the feat at 5-6 and a 42nd unforced error into the net saw the veteran behind for the first time in the championship.
"I felt like I have to win the second set," said Federer. "I don't care how I do it, but I have to do it. Cost me the game tonight."
Tsitsipas called the trainer in the changeover after the seventh game of the fourth set as he began to cramp on a warm and sticky night.
Federer couldn't take advantage of his opponent's plight and Tsitsipas sealed the win on his first match point in the third tiebreak of the match.
"I lost to a better player who was playing very well tonight," said Federer. "Hung in there, gave himself chances at some point, stayed calm.
"It's not always easy, especially for younger guys. Credit to him for taking care of that."
Tsitsipas will meet Spain's 22nd seed Roberto Bautista Agut in the quarter-finals.
"This win is a good milestone, let's say good first step to something bigger," said Tsitsipas.