The second seed recovered from a leg injury to win 7-6 (7-2) 3-6 6-4 to land a major title at the 43rd attempt.
Wozniacki was in tears after grabbing the win, which came 14 years after her first Grand Slam final defeat.
The Dane will replace Halep as world No 1 in the world rankings on Monday.
Wozniacki was class on the court and class off it as she used her first interview after victory to apologise to her beaten opponent.
Speaking on court with tears in her eyes, Wozniacki said: “I’m sorry, I’m just taking a second here to hug Daphne [the Daphne Akhurst trophy]. I’ve dreamt of this for so many years
“I never cry and my voice is shaking but it’s a very emotional moment.
“I want to congratulate Simona. I know today is a tough day and I’m sorry I had to win.
“I’m sure we’ll have many matches in the future. It was an incredible match and again, yes. I’m sorry.
“Last but not least I want to thank my team and my dad.
“You’ve coached me from the start when I was seven and we’ve had our ups and downs and you’ve been by my side every step of the way, so thank you.
“I want to thank my fiancee who is here tonight. Without your support, I was a nervous wreck this morning but you managed to calm me down and help me enjoy this moment.
“Thank you so much for being here and having that special moment with me.”