Federer came through a three-set thriller at London’s 02 Centre – 7-6 (8-6), 5-7, 6-1.
The Swiss world number two has now booked his place in the semi-finals, with just one round robin match to play against Wimbledon finalist Marin Cilic.
Zverev, who beat Federer earlier this year in the final of Montreal Masters, has reached third spot in the world rankings at the age of just 20.
Federer’s route to the final was made easier after Rafael Nadal pulled out of the tournament on Monday through injury.
And Federer feels Zverev has a long and bright future in the game.
“You know exactly what you need to work on in the off season and then coming back stronger next year and that is what will happen with Alex,” Federer said.
“I’m very excited for his future.
“He’s a wonderful guy and also a great, great player.”
Speaking about his swift progress into the last four, Federer added: “I’m happy and relieved that I can play freely against Cilic, instead of it being a nail-biter.
“It’s been a tough group so to be through in two matches is great.”
Meanwhile, in the other group match today, Jack Sock beat Marin Cilic in three sets – 5-7, 6-2, 7-6 (7-4).