Tsitsipas, who is 17 years younger than the Swiss legend, became the first Greek to reach the quarter-finals of a Grand Slam event. He will take on the 22nd seed Roberto Bautista Agut from Spain who got past last year's finalist Marin Cilic in five sets.
"There's nothing really I can say to describe this," said Tsitsipas after his first encounter with Federer.
"Roger has done so much for our sport," he added. "Being on Rod Laver Arena and also playing him ... it's a dream come true."
Tsitsipas – touted as one of the next big things – showed guile and guts against a player seeking a record seventh Australian Open crown. He warded off 12 break points during the encounter.
"I told myself to stay aggressive and I didn't lose patience," he recalled of the crucial moments in the match. "I think that was the key to saving the break points. I showed great fighting spirit."
Federer, who announced that he will play at the French Open for the first time since 2015, was gracious in defeat. "I lost to a better player who was playing very well, who hung in there and stayed calm."
In another coup for the circuit's young guns, unseeded American Frances Tiafoe celebrated his 21st birthday with a muscular four-set win over 20th seed Grigor Dimitrov from Bulgaria.
Tiafoe advanced to his first quarter-final appearance at a Grand Slam 7-5, 7-6, 6-7, 7-5. He will next play the second seed Rafael Nadal.
The 32-year-old Spaniard registered his 20th win in 24 meetings with Tomas Berdych 6-0, 6-1, 7-6.