The 23-year-old secured the Birmingham Classic title with a 6-3, 7-5 win over her German rival, after a match that lasted for an hour and 28 minutes, to secure the world number one spot, reported Efe news.
"It's a dream come true to be the world number one," Barty said after the win.
"My team and I have put in so much work and I'm very proud of what we have achieved."
The Aussie player continued her brilliant streak to claim the 2019 Roland Garros crown a couple of weeks ago, which was her first ever Grand Slam career title.
Barty is set to top the WTA ranking for professional women tennis players with 6,540 points, ahead of Osaka who is to fall to world number two with 6,377 points.
"It's an honor to be in this position, which has been held by the legends of our sport who I respect and admire greatly," she added.
Barty thanked Goerges, with whom she formed a doubles team reaching the Birmingham semis.
"I couldn't think of a better person to share the court with," she told Georges during the trophy ceremony.
"We had an incredible week in singles and doubles. You're one of my best friends on tour."
Georges said: "It was a high-quality match and Ash deserves the win."
Since the beginning of the WTA ranking in 1975, only one Australian player has held the top spot.
That was Evonne Goolagong who was world number one for two weeks in 1976.
Barty became the second Australian and the 27th player overall to top the classification, an achievement made all the more impressive after her 2014 decision to pause her tennis career and become a professional cricket player.
She decided to return to tennis two years later and she is to be at the top of the sport on Monday.
"Ash and I have been together from day one of her tennis comeback and I have loved every minute of our partnership - the successful moments, the challenges and everything in between," Barty's coach, Craig Tyzzer, said.
"She is a truly impressive person and deserves every success that comes her way. I couldn't be prouder to be her coach."
Barty extended her winning streak to 12 in a row, "becoming the first player in 2019 to clinch three WTA singles titles," according to the WTA website.
( With inputs from IANS )