Emily Blunt, Paul Dano and Jeff Daniels will also star in the film, which will be released on September 28.
Looper follows a killer named Joe (Gordon-Levitt) who works for the mob and takes down people who are sent from the future. The plot focuses on Joe spotting an older version of himself (Willis) coming back in time.
On Gordon-Levitt using a combination of make-up and imitation to resemble a young Bruce Willis, director and writer Johnson told the Los Angeles Times: "That was really scary because you commit to that and there's no real way out of it.
"But the biggest thing is Joe's performance, he's really doing Bruce in a big and daring way, but he strikes a balance between obviously imitating Bruce and also building this organic performance."
Gordon-Levitt added that the film will focus more upon the situation that arises from time travel, rather than time travel itself. He said: "If you just tell somebody the plot, you're inevitably telling them the time travel stuff, but the movie actually uses that as a set-up.
"The best parallel I can draw is to the first Terminator movie where time travel is used to set up this impossible situation between these people and then that situation plays itself out."
Joseph Gordon-Levitt will appear in The Dark Knight Rises when it hits cinemas on July 20.
Watch the trailer for The Dark Knight Rises below: