The 50-year-old actor and Heard, who stars in the film, were seen kissing and holding hands as they posed for pictures and strutted on the red carpet.
The 27-year-old actress and the Pirates of the Caribbean star made their first official public appearance together last month after dating for more than a year.
Other than for promoting their joint film The Rum Diary in 2011, Wednesday marked the first night the couple walked the red carpet together as an item.
Rumors that Heard and Depp are engaged to be married began last month after the actress was spotted wearing a sparkly jewel on her ring finger.
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