Scott, an ex-footballer for Arsenal and England, says she had a relationship with Smith when she was a young player.
The broadcaster has spoken about their relationship for the first time, as she prepares to open up about intimate details in her new book, How (Not) To Be Strong.
She says it was a big decision to write about her relationship with Smith but the 37-year-old claimed it would be like "cheating" if she kept it secret.
Speaking about the book during an event in east London, she said: “I went back and forth on whether I’d actually be writing the chapter.
Alex Scott playing for England
PA Features Archive/Press Association Images
“But then it was one of those moments, I’m writing this book and I want to tell everything.
"I thought I’d be cheating you all if I didn’t put that in there.
"And for me, it’s like that first love story, I fell madly and deeply in love.
“And yes, there’s that heartbreak and those things, but it’s a huge part of my life and I wouldn’t go back and change that.
“Because that feeling of love and that excitement and what it gives you, it needed to be in there.”
Scott has never spoken about her sexuality before but friends say she is open to dating both men and women.
She met Smith when they played for Arsenal in 2005.
They both signed for US side Boston Breakers in 2009 before moving back to the UK three years later to join Team GB's women's football team at the London Olympics.
Smith is married and has two children with management consultant DeAnna Dobosz.
In an interview over the weekend, Scott said she has been single "for a while" because she "needed to be" but is now "ready to be loved".
Alex Scott and Kelly Smith
PA
