The Court of Appeal rejected Associated Newspapers' attempt to have a trial in the privacy and copyright case.
Meghan said it was a win "not just for me, but for anyone who has ever felt scared to stand up for what's right".
Associated Newspapers said it was disappointed, and was considering a further appeal to the Supreme Court.
A judge had previously ruled in favour of Meghan after extracts from the letter appeared in the paper.
In a statement issued after the ruling, the duchess urged people to be "brave enough to reshape a tabloid industry that... profits from the lies and pain that they create".
Meghan, who started the civil action against newspaper group in 2019, said: "In the nearly three years since this began, I have been patient in the face of deception, intimidation and calculated attacks."
She added: "The courts have held the defendant to account and my hope is that we all begin to do the same. Because as far removed as it may seem from your personal life, it's not. Tomorrow it could be you.
"These harmful practices don't happen once in a blue moon - they are a daily fail that divide us and we all deserve better."