Muguruza announced her talent to the world two years ago by handing Williams her heaviest ever slam loss in the second round of the French Open and then lost to the American in her first final at Wimbledon last summer.
Williams failed to add to her 21 major titles since beating Muguruza at Wimbledon past year and remains behind Steffi Graf's Open-era record of 22.
"I'm so excited. To play a final of a grand slam against one of the best players, I'm so happy".
"That just goes to show you you really have to play the big points well, and I think she played the big points really well", Williams told reporters.
"I think she has the desire", he said.
Garbine Muguruza won her first Grand Slam Saturday at the French Open.
Spain's Garbine Muguruza holds the cup after defeating Serena Williams of the USA after their final match of the French Open tennis tournament at the Roland Garros stadium, Saturday, June 4. Women's tennis badly needed a charismatic new champion to shake up the era of Williams and Maria Sharapova, whose doping verdict is likely to arrive this week.
With the victory, Muguruza came out the first Spaniard winning at Roland Garros after Rafael Nadal in 2014, and the first Spanish woman to become a champion here since Arantxa Sanchez Vicario, in 1998. Today was a day that, yes, Serena didn't have her A game, but she finds a way to win with her B game. "She knows how to play on the big stage and she knows how to. clearly she knows how to win grand slams".
"You know what I thought?"
"If she was indifferent about making history in her sport that would be a concern", Mouratoglou said.
A weak Williams backhand put Muguruza up a break in the second, only for the Spaniard to serve consecutive double faults as the American broke back for 1-1.
Chance number three to draw level with Graf came on Saturday in Paris, against fourth seed Muguruza, who Williams beat at Wimbledon in 2015 to win title number 21.
"They key? I just have a very aggressive game", said Muguruza, whose three career tournament titles are 67 fewer than Williams' total. "She has nothing to prove at this point, she's just playing for record books".
Here's a look at those six final losses in Williams' Grand Slam career. Backed into a defensive corner, she lifted a gentle, arching topspin lob that curled into the sky and fell back to the red clay inside the baseline for match point.
Williams refused to blame her adductor injury and said the pressure of trying to match Graf was not a factor either.
On Monday, Muguruza, whose hard-hitting game is at its devastating best on fast courts, will be second in the WTA rankings going into the grass season. "She's so good. I think she is going to be very good for tennis and for Spain, it will be like Santana in 1961". It's our favourite tournament in Spain and I want to thank all my Spanish supporters.
She will next play in Mallorca, to tune up for Wimbledon, where she finished runner-up behind Williams previous year.