In an enthralling encounter that lasted just over three hours, the American beat the Olympic champion 3-6 6-4 7-6 (7-2) in Saudi Arabia.
At 20 years old, she is the youngest player to win the tournament since Maria Sharapova exactly two decades ago, and the youngest American since Serena Williams in 2001.
“This means a lot to me,” said third seed Gauff, who wins a total prize of $4.8m (£3.7m) – a record amount in women’s professional tennis.
“This is the first professional women’s tennis event here in Saudi Arabia and I’ll forever be etched in history in that standard.”
Speaking earlier to Sky Sports, she said: “That was a great match. I was just trying my best to hang in there and I never gave up.”
In progressing to Saturday’s showpiece in Riyadh, Gauff had become the youngest player to reach the championship match at the WTA Finals since Caroline Wozniacki in 2010.
She had seen off both the world number one and two in Aryna Sabalenka and Iga Swiatek en route to the final, and piled the pressure on her opponent in the early stages against Zheng.
In what was only their second meeting – Gauff having won their first in straight sets in Rome earlier this year – Zheng, 22, was forced to save four break points, including three in a captivating fifth game.
But it was the Chinese seventh seed who got the decisive break in the opener, a double fault from Gauff after a hat-trick of unforced errors giving Zheng the advantage from which she sealed the set as Gauff slammed a backhand into the net.
Zheng’s serve is one of her greatest weapons, but she struggled to show it off against Gauff, with her first of only four aces coming at the start of the second set after she had broken Gauff again.
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