Born and raised in Sydney, Gillespie moved to New York City at the age of nineteen[1] to study illustration, graphic design and advertising at Manhattan's School of Visual Arts.

[2] His commercial for Snickers featuring Betty White playing backyard football was voted the top ad of Super Bowl XLIV by USA Today and is credited with renewing public interest in the actress.

[1] He had first read the script before he was attached to Mr. Woodcock, but the pitch for Lars and the Real Girl—a man falling in love with a sex doll—which he had almost turned down himself, believing the premise to be an "absurd notion",[1] put off many major studios.

[9] Gillespie directed several episodes, including the pilot, of the first season of Steven Spielberg and Diablo Cody's television series The United States of Tara.

In March 2010, it was announced that Gillespie would direct the Fright Night remake,[12] starring Colin Farrell, Anton Yelchin and Toni Collette for the lead roles.

In April 2014, it was announced that Gillespie would direct the film The Finest Hours about the Coast Guard who tries to save the crews of two oil tankers in 1952.

Chris Pine, Casey Affleck, Josh Stewart, Graham McTavish and Kyle Gallner star in the film for Walt Disney Pictures.

[27] In April 2022, Gillespie signed on to direct a film adaptation of Ben Mezrich's book The Antisocial Network, about the GameStop short squeeze for Metro-Goldwyn-Mayer.