As asked on Quora:
Luke learns that he is Vader's son privately and finds out Leia is his sister in a separate revelation. Are these 2 points ever revealed to Leia, and what is her reaction to learning that the person who imprisoned her, tortured her, and destroyed her home planet is her father?
Yes, Luke tells her in The Return of the Jedi, on a footbridge in the Ewoks village.
First, he tell her that Vader is his father:
LEIA Luke, tell me. What's troubling you?
LUKE Vader is here...now, on this moon.
LEIA (alarmed) How do you know?
LUKE I felt his presence. He's come for me. He can feel when I'm near. That's why I have to go. (facing her) As long as I stay, I'm endangering the group and our mission here. (beat) I have to face him.
Leia is distraught, confused.
LEIA Why?
Luke moves close and his manner is gentle. And very calm.
LUKE He's my father.
LEIA Your father?
Immediately after, he tells her that she is his sister (and thus Vader's daughter).
LUKE There's more. It won't be easy for you to hear it, but you must. If I don't make it back, you're the only hope for the Alliance.
Leia is very disturbed by this. She moves away, as if to deny it.
LEIA Luke, don't talk that way. You have a power I--I don't understand and could never have.
LUKE You're wrong, Leia. You have that power too. In time you'll learn to use it as I have. The Force is strong in my family. My father has it...I have it...and...my sister has it.
Leia stares into his eyes. What she sees there frightens her. But she doesn't draw away. She begins to understand.
LUKE Yes. It's you Leia.
LEIA I know. Somehow...I've always known.
