The couple met while making "The Rum Diary," an adaptation of journalist Hunter S. Thompson's "lost" autobiographical novel of the same name.
"They are 100 percent dating," a source told US Weekly. "He treats her really well." A friend says the twosome "started sleeping together during the press tour."
Heard, 26, previously came out as a lesbian at the Gay and Lesbian Alliance Against Defamation 25th anniversary celebration. She was previously linked to artist Tasya van Ree.
This past spring Depp bought Heard a horse so the couple could ride together in New Mexico.
Heard recently starred in the now defunct TV series "The Playboy Club" and Depp appeared in the film "Dark Shadows."