The Sweet Story Behind Martina Navratilova's Marriage Proposal

Martina Navratilova (left) and Julia Lemigova

Tim Whitby/Getty

By Elizabeth Leonard

@lizzleonard1

09/10/2014 AT 12:20 PM EDT

It was never a question of if. It was the where, when and how that proved tricky.

For months, Martina Navratilova mulled the best way to pop the question to her longtime girlfriend, Julia Lemigova, and, in the end, she went big. Very big.

"Originally it wasn't the idea to do it at the U.S. Open, on the Jumbotron and all that, but then it was, 'Why not? I've seen it in movies!' " Navratilova, 57, tells PEOPLE exclusively of her Sept. 6 proposal that was telecast live during the tennis championships at New York's Arthur Ashe stadium. "And it all came off, everything worked out perfectly!"

While the couple, who have been dating since 2006, toasted with champagne after a teary Lemigova, 42, said "yes," the more poignant celebration came later. "What's been amazing is the outpouring of support from everywhere, including when I was walking through the stadium afterwards with people saying, 'Congratulations,' people on the street saying, 'Congratulations,' and the Twitter outpouring has been unbelievably supportive," the tennis legend marvels.

"The changes in people's attitudes [on gay marriage] is amazing. You put it out to the world and it already feels like we're married because the whole world knows."

For the 59-time Grand Slam winner, taking this step with Lemigova, a past Miss USSR, was a no-brainer.

"She's just a special human being inside and out," says Navratilova of her fiancée. "[I love] her dimples when she smiles. She's got a honey voice and a honey personality. We've come from similar backgrounds and experiences in life and we've both overcome a lot. We both dreamt big and we both made it, so it's pretty cool!"