Serena, 35, won 6-4 6-4 to pass Steffi Graf in the all-time list of major winners since the Grand Slams accepted professional players in 1968.
The American regains the number one ranking from German Angelique Kerber.
Australia's Margaret Court, with 24, is the only player still ahead of Serena in terms of Grand Slam singles titles.
"Congratulations Serena on number 23," said Venus, who at 36 is the oldest Australian Open finalist in the Open era.
"I have been right there with you, some of them I lost right there against you. It's been an awesome win.
"I'm enormously proud of you, you mean the world to me. I, God willing, would love to come back. Thank you for all the love."
Serena paid tribute to her sister, who was playing her first major final for eight years, saying: "There's no way I would be at 23 without her. There's no way I'd be at one without her. She's my inspiration.
"She's the only reason I'm standing here today. She's the only reason the Williams sisters exist. Thank you for inspiring me. Every time you won this week, I felt like I got a win too."