The 18-year-old Russian, who won back-to-back WTA 1000 titles last year in Dubai and Indian Wells, will meet Paris Olympics silver medallist Donna Vekic in the opening round at Melbourne Park.
Mboko, 19, raced to a 3-0 lead but Andreeva turned the tables to reel off the next six games to take the opening set.
It was one-way traffic in the second set as Andreeva broke early to take the opening three games and sealed the match on serve, setting herself up perfectly for the year's opening Grand Slam, which begins on Sunday.
Andreeva joked at the presentation ceremony that her team, which includes coach and former world number two Conchita Martinez, had little to do with her win.
"I do feel like it was all me," she said. "I’ve been practicing a lot. I’ve been working, sweating, and I don’t even know why you’re here, honestly.
"I want to thank myself for being brave in all the matches I played. I want to thank myself for pushing myself every day in practice ... I want to thank myself for changing my mentality for fighting till the very last point.
"For doing what I've got to, doing what my team tells me to do, sometimes with complaining, but it’s OK."
In the Auckland men's final, Jakub Mensik beat Sebastian Baez 6-3, 7-6(7) to collect his second ATP title after his breakthrough triumph at last year's Miami Open, where the 20-year-old beat mentor Novak Djokovic in the final.
Mensik opens his Australian Open campaign against Spain's Pablo Carreno Busta, while Baez meets big-serving Frenchman Giovanni Mpetshi Perricard.
Italy's Elisabetta Cocciaretto beat American Iva Jovic 6-4, 6-4 in another tune-up tournament in Hobart for her first WTA title since 2023.