"Meeting her and getting to know her was a real pleasant surprise," the actor, 47, who stars with Jolie in the upcoming film The Tourist, tells rocker Patti Smith in an interview for Vanity Fair.
"You don't know what she might be like – if she has any sense of humor at all. I was so pleased to find that she is incredibly normal," he added, "and has a wonderfully kind of dark, perverse sense of humor."
In fact, Depp, a three-time Oscar nominee, compares Oscar winner Jolie, 35, to another Hollywood leading lady – one from an earlier generation.
"I've had the honor and the pleasure and gift of having known Elizabeth Taylor for a number of years," Depp says. "You know, you sit down with her, she slings hash, she sits there and cusses like a sailor, and she's hilarious. Angie's got the same kind of thing, you know, the same approach."
Depp says he also feels a measure of sympathy for Jolie and her family, who deal with the harshest glare of fame.
"Poor thing, dogged by paparazzi, her and her husband, Brad [Pitt] ... all their kids," he says. "There are times when you see how ridiculous is this life, how ludicrous it is, you know, leaving your house every morning and being followed by paparazzi."
The actor also touches on a number of other subjects, including Disney executives' shocked reaction to his Jack Sparrow performance. "I think it was Michael Eisner … who was quoted as saying, 'He's ruining the movie,' " says Depp, who also talks about his early dreams of being a rock star. "I was a guitarist, and that's what I wanted to do."
And he reveals what could be an interesting future project. "[Marlon Brando said,] Why don't you just take a year and go and study Shakespeare, or go and study Hamlet. Go and work on Hamlet and play that part. Play that part before you're too old ... And I would like to. I'd really, really like to."