After appearing in British stage plays and TV, the 33-year-old British actress finally got her big break by piling on two stone to play Benny in Circle Of Friends.
Audiences were intrigued to find that beneath the ugly duckling fatness was, in reality, a gorgeous woman with an hour-glass figure.
She headed for Hollywood and made it big in such films as Sleepers, Big Night, Grosse Pointe Blank, and Good Will Hunting.
She has just completed filming Ella Enchanted, a modern-day fantasy featuring fairies, ogres and elves. She is currently filming the movie version of Andrew Lloyd Webber's hit musical Phantom Of The Opera.
The Oscar-nominated 5ft 10in star was most put out when she found that the bottom used in The Governess was not her own. "I am very proud of my bottom!" she says.
"I want everyone to know that it's not my bottom you get to see on the screen because mine is much nicer."
She's happy with her shape right now, but admits that she might consider plastic surgery "20 years from now". But breast implants are definitely out.
Not a conventional beauty in Hollywood terms, she is still stunningly attractive with her reddish-brown pre-Raphaelite curls, green eyes, voluptuous figure and never-ending legs.
Exercise:
Minnie works out two hours a day, five days a week with a personal trainer.
"If I'm not working, working-out gives me a real focus. If I don't like the way I am, I can change it."
She's also taken up boxing. "I box on Saturdays. No sparring, just shadow-box training."
Diet:
"I am no obsessive about food, but careful when I have to be. I stay slim by keeping a watchful eye on my calorie intake. I'm a fat person in a thin body or a fat body, and I always will be."
Love-life:
She has a habit of falling in love with her leading men - with disastrous results. First she fell for John Cusack, her co-star in Grosse Pointe Blank, and just when she thought they were getting serious, he ended their relationship.
Then, famously, she fell for her Good Will Hunting co-star Matt Damon, but he dumped her on Oprah.
In 2001 she became engaged to actor Josh Brolin, but that also broke up.
Now she is reported to be dating 21-year-old US tennis player Robby Ginepri.