Federer, the oldest man in the field at 38, was beaten by the youngest as Tsitsipas swept into the final 6-3 6-4.
For the second year running the 20-time grand slam champion was taken out by a 21-year-old at the semi-final stage.
Twelve months ago it was Alexander Zverev who accounted for the Swiss master and this year sixth seed Tsitsipas sent him packing.
The changing of the old guard may be taking its time – Rafael Nadal, Novak Djokovic and Federer once again ended the year as the top three – but it is definitely on its way.
Tsitsipas, clearly finding the zippy hard courts at London’s 02 to his liking, showed no ill-effects despite battling with Nadal for nigh on three hours on Friday afternoon.
Federer, meanwhile, was unable to reach the heights he scaled while dismantling Novak Djokovic two nights ago.
He had his chances, though, creating no fewer than 12 break points, but only managing to convert one of them.
That should have come as no surprise, however, as in their previous three meetings Federer had forced 22 break points and Tsitsipas saved 18 of them.
Tsitsipas warded off another six in the opening set while taking his only one in the second game, burying a forehand down the line.
He served for the set at 5-3, but with Federer briefly looking more tuned in, it took the youngster 15 minutes and seven set points to get over the line.
An error-strewn start to the second set from Federer handed Tsitsipas another break but the eight-time Wimbledon champion pulled it straight back, finally winning a break point at the 10th attempt.
But a third break in a row saw Tsitsipas seize the initiative once more, frustration etched on Federer’s face as he shanked a routine backhand wide before a forehand whizzed past him.
Federer kept the pressure on as Tsitsipas served for the match, but once again the man from Athens saved break points, two of them, before finishing the job with an ace.
Tsitsipas said: “I’m so proud of myself today, it was a great performance.
“Sometimes in matches like these you wonder how you recover from difficulties and break point down.
“It is a mental struggle and I’m proud how many I saved today, I was trying not to give Roger an easy time.
“He was an inspiration as always. Playing him is the biggest honour I can have and today’s victory is probably one of my best moments of the season.”
It was the 16th time in 17 appearances that Federer had made the last four, but he was unable to reach his 11th final.
“I’m frustrated I couldn’t play better and when I did and fought my way back, I threw it away again,” he said.
“It was also parts of him. He did come up with the goods when he had to and he was better than me today.
“It’s the year-end. It’s over now and I can’t make it better. I knew he was going to be incredibly athletic. He was just a little bit better today at all those little things.”
Meanwhile Tomas Berdych, the 2010 Wimbledon runner-up, has announced his retirement at the age of 34.