He was born in Heywood, Greater Manchester, and is the twin brother of Luke Tittensor with whom he starred in Brookside and the first season of Shameless.
In 2003, Elliott and his twin brother Luke had a brief appearance in Brookside as Terry Gibson's twin sons.
In 2004, Elliott and his brother Luke were cast in the shared role of Carl Gallagher in the dramedy Shameless. Elliott took over the role entirely when Luke left the show to become a regular on soap drama Emmerdale.
In addition to his role in Shameless, Elliott has appeared in an episode of the BBC drama miniseries Moving On. He has also appeared in episodes of Silent Witness and starred in short film Protect Me From What I Want playing a gay character.
In January 2010, Elliott appeared on the cover of Attitude magazine. He also appeared in the video for Plan B's Stay Too Long and The Ruskin's Old Isleworth, alongside his partner, actress Kaya Scodelario. He has also appeared in the video for Coldplay's Charlie Brown.
Elliott revealed on Twitter that he was set to return to Shameless for the final episode of the final season alongside Jody Latham.
Elliott completed filming a new film about The Stone Roses called Spike Island, which was released in June 2013.