01/23/2014 AT 10:25 AM EST
Sure, they had onscreen chemistry in 2011's The Rum Diary
, but sources close to newly engaged
couple Johnny Depp
and Amber Heard say their connection is much more than physical.
"Amber is a female version of Johnny," says a longtime Depp friend. "She's sort of kooky and outspoken, and while that would intimidate many guys, it is a turn-on for Johnny."
It isn't as if Depp, 50, the cool, bohemian bachelor twice crowned PEOPLE's Sexiest Man Alive, hasn't been smitten before – he's had very public romances with the likes of Winona Ryder
, Kate Moss
and Vanessa Paradis
, with whom he has children Lily Rose, 14, and Jack, 11. But now he's utterly head over heels
for Heard, 27.
At the Art of Elysium gala on Jan. 11, where the couple made their first major public appearance together
, Depp was "following her around" throughout the evening, says an acquaintance of his. "He looked lovestruck."
The Austin, Texas-born Heard, who has been open about her bisexuality, tumbled hard for Depp, too. "She really just fell in love with him," says a friend. "She's a sweet girl. She's an old soul and he's older, so it makes sense that she'd fall for him."
For much more on Heard's surprising past, their secretive romance and why Depp decided to pop the question, pick up the new issue of PEOPLE, on newsstands Friday