The German, the youngest finalist in nine years at just 21, showed immense confidence in a high-quality final as he dispatched the 14-time Grand Slam champion 6-4, 6-3.
The victory marks a big moment in the career of Zverev as he finally delivered on the promise that has seen him win three Masters titles and become the shining light of a 'next generation' of up-and-coming tennis stars looking to upset the established order.
In a hugely entertaining first set both players showed the excellence that had brought them to this final stage after impressive seasons.
In the first set Zverev offered up fearless tennis, staying solid behind his huge serve, crushing down big groundstroke winners and taking on Djokovic at the net with a series of drive volleys.
The Serb barely made an error early on and defended manfully to get the better of the long rallies, but the German world No. 4's confidence was undiminished.
He finally struck at 4-4, profiting from a pair of uncharacteristic errors on the suddenly brittle Djokovic forehand to earn the break of serve.
It was the first time the world No. 1 had been broken all week and he was unable to bounce back as Zverev smashed down three massive aces, among 18 of 21 points he won on serve, to take the first set.
Djokovic was quickly in deep trouble at the start of the second as a pumped-up Zverev out-rallied him to earn another break point, and duly converted with a magnificent forehand winner after a pulsating back-of-the-court rally.
The momentum shifted slightly in the next game as Zverev hit loose back-to-back double faults to let Djokovic back in, but he was unaffected, again exerting immense pressure on the Djokovic serve to break for the third time in a row and re-take the lead.
Zverev made a vital hold from 0-30 down at 3-2, picking up a beautiful volley near his feet as Djokovic fought desperately to regain parity.
But the former champion was unable to wrestle control from the powerful Zverev, who held serve well and then took advantage of a tired Djokovic service game, finishing off with a magnificent backhand winner down the line.
Zverev upsets the odds
"I am unbelievably happy. This is the biggest title I have won," said Zverev.
"I want to congratulate Novak on a great week and how you played in the second half of the season. We have never seen it before. You barely lost a match I am actually very happy you lost one this week!"
"The crowd have been absolutely amazing all week. I appreciate you all coming out to support and show love for the sport.
"It makes it so much easier for us to play so thank you for that."
Zverev became the first German champion since Boris Becker won in Frankfurt in 1995.
He recovered wonderfully from the controversy surrounding his semifinal victory over Roger Federer, when he was booed for stopping mid-rally when a ball-boy dropped a ball in his vision.
That win was itself a huge scalp for a player that has never gone beyond the quarterfinals at a Grand Slam, but here he went one better.
This breakthrough win meant he became just the fourth player to beat Federer in a semifinal and Djokovic in a final in the same tournament. The others are Andy Murray, Rafael Nadal and David Nalbandian.
More than just the title, the way he overcame those world-leading players is likely to be a source of huge confidence for the German as he looks to improve his Grand Slam record in 2019.
Djokovic falls short after wonderful year
Novak Djokovic was aiming for a record-equalling sixth title to move level with Roger Federer, but he was unable to replicate the breathtaking form that saw him win every service game in his first four matches in London.
Although he came up against an inspired opponent in Zverev, Djokovic faltered particularly on his forehand and never managed to dictate play in the final.
He had been imperious up to that point, beating Zverev in straight sets during the group stage, but admitted his opponent's improvement had been crucial.
"Sascha [Zverev] definitely played much better than he did in the group stage. He deserved to win, he's still quite young but he's had an amazing career so far and I wish him all the best for his future," said Djokovic.
"Speaking of being young, hopefully I'll play many more years and I'll see you guys here in years to come.
"I want to thank my team for a great season. If we put things in perspective, it was an amazing year, a great comeback so thanks for helping me get to where I am.
"Thank you to the fans for supporting tennis for 11 months. It's a long season but you guys making it very enjoyable for all of us."
It has still been a great year for Djokovic, who recovered from a slow start to win the US Open and Wimbledon in a wonderful summer.