Answer by taking a quote from the following article:

Woo was born Wu Yu-seng (Ng Yu-sum in Cantonese) in Guangzhou, China, amidst the chaos of the Chinese Civil War at the end of October 1946. Due to school age restrictions, his mother changed his birth date to 22 September 1948, which is what remains on his passport. The Woo family, Christians faced with persecution during Mao Zedong's early anti-bourgeois purges after the communist revolution in China, fled to Hong Kong when he was five. Impoverished, the Woo family lived in the slums at Shek Kip Mei.

An emigre in 1993, the director experienced difficulty in cultural adjustment while contracted with Universal Studios to direct Jean-Claude Van Damme in Hard Target. As characteristics of other foreign national film directors confronted the Hollywood environment, Woo was unaccustomed to pervasive management concerns, such as limitations on violence and completion schedules. When initial cuts failed to yield an "R" rated film, the studio assumed control of the project and edited footage to produce a cut "suitable for American audiences". A "rough cut" of the film, supposedly the original unrated version, is still circulated among his admirers.  A three-year hiatus saw Woo next direct John Travolta and Christian Slater in Broken Arrow. A frenetic chase-themed film, the director once again found himself hampered by studio management and editorial concerns. Despite a larger budget than his previous Hard Target, the final feature lacked the trademark Woo style. Public reception saw modest financial success.  Reluctant to pursue projects which would necessarily entail front-office controls, the director cautiously rejected the script for Face/Off several times until it was rewritten to suit him. (The futuristic setting was changed to a contemporary one.) Paramount Pictures also offered the director significantly more freedom to exercise his speciality: emotional characterisation and elaborate action. A complex story of adversaries--each of whom surgically alters their identity--law enforcement agent John Travolta and terrorist Nicolas Cage play a cat-and-mouse game, trapped in each other's outward appearance. Face/Off opened in 1997 to critical acclaim and strong attendance. Grosses in the United States exceeded $100 million. Face/Off was also nominated for an Academy Award in the category Sound Effects Editing (Mark Stoeckinger) at the 70th Academy Awards.  In 2003, Mr. Woo directed a television pilot entitled The Robinsons: Lost in Space for The WB Television Network, based on the 1960s television series Lost in Space. The pilot was not purchased, although bootleg copies have been made available by fans.  John Woo has made three additional films in Hollywood: Mission: Impossible 2, Windtalkers and Paycheck. Mission: Impossible 2 was the highest-grossing film in America in 2000, but received mixed reviews. Windtalkers and Paycheck fared poorly at the box office and were summarily dismissed by critics. Woo directed and produced a videogame called Stranglehold for games consoles and PC. It is a sequel to his 1992 film, Hard Boiled. He also produced the 2007 anime movie, Appleseed: Ex Machina, the sequel to Shinji Aramaki's 2004 film Appleseed.

When did he go to the USA?