Naomi Osaka 7-6 (7-2) 5-7 6-4 Petra Kvitova
Kvitova saves three championship points to force third set
Osaka becomes world number one after winning back-to-back Grand Slam titles
We're going to leave this live text here.
There's a report of that magnificent final over here and if you missed any of it, there's highlights on BBC One at 13:15 GMT.
We'll be back tomorrow, when Novak Djokovic and Rafael Nadal try to top the drama of this match.
Until then...
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Australian Open champion and world number one.
What a player.
Image source, AFPPetra Kvitova will leave Melbourne as the world number two.
This time last year, she went on a 14-match winning streak.
I suspect 2019 will hold more of the same.
Image source, Reuters#bbctennis
Jeanna Louise Skinner: I want to be Naomi Osaka when I grow up. I'm 41.
Josh Peters: Petra, you're such an inspiration, hard luck.
Abisoladot: Congrats Naomi simply a great performance and we are proud of the great player you are becoming.
Image source, Getty ImagesKvitova 6-7 (2-7) 7-5 4-6 Osaka
More from Naomi Osaka: "I want to thank everyone, you make this tournament possible. Thanks to my team (nervous giggle). I don't think I would have made it through this week without you. Behind a tennis player is always a great team so thank you.
"I read notes before this but I still forgot what I was meant to say! Thank you everyone, I am really honoured to have played in this final."
Petition for Naomi Osaka to give all speeches forever.
Kvitova 6-7 (2-7) 7-5 4-6 Osaka
Australian Open champion Naomi Osaka: "Erm, hello. Sorry, public speaking isn't my strong point so I hope I can get through this!
"I wouldn't have wanted this to be our first match but huge congratulations to you [Kvitova] and your team. You are amazing and I am honoured to have played you in a Grand Slam final.
"Thank you for coming and watching. It's really hot all the time."
*She pauses to hand over the trophy to someone*... "Oh thank you!"
Image source, Getty ImagesKvitova 6-7 (2-7) 7-5 4-6 Osaka
Russell Fuller
BBC tennis correspondent at Melbourne Park
What happens at Roland Garros you wonder?
Kvitova 6-7 (2-7) 7-5 4-6 Osaka
More from Petra Kvitova: "It has been a great tournament for me. Of course I need to thank my family and friends. They were supporting me throughout. Thank you to everyone who made this possible. I always love to come back and play here.
"And to my team, thank you for everything. But mostly, thank you for sticking with me even though we didn't know if I was able to hold a racquet again.
"You were supporting me every single day and staying positive for me which I really needed. It wasn't easy so thank you so much. Hopefully we'll be healthy and we'll see you next year."
Image source, Getty ImagesKvitova 6-7 (2-7) 7-5 4-6 Osaka
Runner-up Petra Kvitova: "It's crazy. I can't believe I have just played in the final of a Grand Slam again.
"It was a great final. Well done Naomi. To her team as well, you really played well. Congratulations for being world number one as well."
"Um, hello! Public speaking isn't really my strong side," says Naomi Osaka.
She's great.
Kvitova 6-7 (2-7) 7-5 4-6 Osaka
Kvitova thanks her team for standing by her "even when we didn't know if I would be able to hold a racquet again".
She tears up, and the crowd give her a long standing ovation as she composes herself.
Image source, ReutersKvitova 6-7 (2-7) 7-5 4-6 Osaka
A member of the crowd shouts out "we love you, Petra!"
"Thank you!" is the reply.
Kvitova 6-7 (2-7) 7-5 4-6 Osaka
Petra Kvitova is coming up receive her runner-up trophy.
She stops to talk to the young tennis player who is up on the stage, and then she gets a hug off Li Na.
#bbctennis
Pravesh Dodia: Osaka, Osaka, Osakaaaa! Truly deserved! Amazing performance from both ladies! Absolute athletes!
Jackie Clarke: Well done to her. My goes out to Kvitova... Don't worry, Wimbledon is waiting for you..
Kvitova 6-7 (2-7) 7-5 4-6 Osaka
Li Na will be presenting Naomi Osaka with the Australian Open trophy.
Meanwhile, a word from Osaka's coach, Sascha Bajin...
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Kvitova 6-7 (2-7) 7-5 4-6 Osaka
The winning moment.
Image source, ReutersKvitova 6-7 (2-7) 7-5 4-6 Osaka
We've just seen a shot of Naomi Osaka going off court at the end of that second set, with tears in her eyes.
To come back from that... it's just remarkable. She played so, so well in that third set.
Kvitova 6-7 (2-7) 7-5 4-6 Osaka
Kim Clijsters
Four-time Grand Slam champion on BBC Radio 5 live sports extra
It's incredible. I am speechless. The way she was able to serve that out and keep her composure after what happened in the second set shows what a great champion she is and that what happened in the US Open wasn't just a one off. She is a great champion and has proven she can be around for a long time. Plenty of Grand Slam finals to come.
Image source, Getty Images