The German left-hander was assured of becoming number one when the new rankings come out on Monday after top-seeded American Serena Williams was defeated by Czech 10th seed Karolina Pliskova 6-2 7-6(5) in the earlier semi-final.
Australian Open champion Kerber, who leads the WTA for most main draw match wins this season at 53-14, clinched victory with a backhand that actually landed just beyond the baseline but went unchallenged by former number one Wozniacki of Denmark.
"It's just incredible. It's a great day," Kerber said on court. "To be here in the final for the first time, that means a lot. To be number one in the world, it sounds amazing."
Kerber will become the second German to top the women's rankings, following Steffi Graf.
"For me, it’s just amazing to be after Steffi the next number one player in Germany," said Kerber, who at 28 will become the oldest player to reach number one.
"Steffi is a great champion, she's a great person. I think she’s proud of me to be the next one after her."
Wozniacki, who has slipped to 74th in the rankings coming back from injuries, saluted Kerber.
"Obviously, she's had a great year," the Dane said. "She gets a lot of balls back. She knows how to change the pace. She gets good angles.
"She's playing really well."
Kerber had downplayed talk about becoming number one but admitted it felt "just great".
"To be now the number one in the world, that was always a dream for me," she added.
The changing of the guard as women's top player also safeguarded Graf's share of the record for most consecutive weeks at number one with Williams at 186.
The derailing of Williams' bid for a record-setting seventh U.S. Open title kept the American stalled at 22 grand slam singles titles - tied with Graf for most in the Open era.
Kerber, who beat Williams in the Australian Open final for her first slam and fell to the same player in the Wimbledon title match, has one unfinished piece of business - getting even with Pliskova, who beat her in last month's Cincinnati final.
"I will try to take the revenge against her," said Kerber, who holds a 4-3 career edge over the big-serving Pliskova.
(Editing by Sudipto Ganguly/Peter Rutherford)
