The 50-year-old "Pirates of the Caribbean" actor confirmed the news days after he was spotted wearing a woman's engagement ring on his left index hand, which set off speculation that he was to wed Heard.
Heard, a 27-year-old Texas native, co-starred with Depp in 2011's "The Rum Diary." The following year, Depp split from his long-time partner, the French actress Vanessa Paridis, with whom he has two children.
Depp, who is currently promoting his new sci-fi film "Transcendence," also called Heard "a wonderful girl. She's sharp as a tack," according to a "Today" transcript released on Thursday.
Depp's representatives did not respond to requests for comment.