Fitzgibbon was born in The Brisbane suburb of Manly on 15 June 1976. Having sailed since the age of five, he joined the Royal Queensland Yacht Squadron in 1990. On 29 March 1997, an incident occurred at the Middle Harbour Yacht Club jetty in which he broke his neck, leaving him a quadraplegic. In 2004 he competed in the Disabled Sailing World Championship, which he won in his class, and was jointly awarded the Disabled Sailor of the Year along with Andrew Hartley.

In 2007, he partnered with Rachael Cox in the SKUD International Championships, where they won a gold medal. They later competed in the IFDS World Championships and placed fifth.They were jointly named as Sailors of the Year with a Disability.

The two teamed up again in the 2008 Beijing Paralympics in the SKUD 18 class and won the silver medal. The class, which premiered at the 2008 games, was created when Fitzgibbon convinced the International Foundation for Disabled Sailing to adapt the class to allow two sailors with disabilities to participate. They were again jointly named the Sailors of the Year with a Disability.

After seeing Liesl Tesch in an SBS documentary about the boat Sailors with Disabilities competing in the Sydney to Hobart Yacht Race, Fitzgibbon contacted her in late 2010 and they formed a sailing partnership. He partnered with Tesch at the ISAF World Cup in January 2011 where they won gold,and at the IFDS World Championships in July, where they won bronze. The pair were jointly named as Sailors of the Year with a Disability, the fourth time Fitzgibbon won the award.

At the 2012 London Paralympics, the pair won a gold medal in the Mixed Two Person SKUD18.