Reardon turned professional from West Bowling to sign for Bradford Bulls in 2000, he shot to prominence in late 2002 when former Bulls assistant coach Karl Harrison took over as head coach of Salford City Reds and signed Reardon to boost the Reds' fight against relegation.
He enjoyed a rapid rise from Academy to Super League and Test rugby league between 2002 and 2004. Though the Reds were unable to escape the drop, Reardon earned a call up to the England 'A' tour of Fiji and Tonga, where he worked with Warrington Wolves coach Paul Cullen.
He returned to the Bulls in 2003 and found a place in the first team after a long term injury to Michael Withers, making 20 appearances in the title-winning Bradford Bulls side, including being fullback in the 2003 Super League Grand Final against Wigan Warriors in which he scored a try. Reardon scored a try and won the Harry Sunderland Trophy for his man-of-the-match performance at the Old Trafford showdown. Reardon represented England 'A' while at Bradford Bulls in the 2003 European Nations Cup against Wales and France. Having won Super League VIII, Bradford played against 2003 NRL Premiers, the Penrith Panthers in the 2004 World Club Challenge. Reardon played from the interchange bench in the Bulls' 22-4 victory. Later that year year Reardon played for the Bradford Bulls on the wing in their 2004 Super League Grand Final loss against the Leeds Rhinos. He broke into the Great Britain squad for the 2004 Tri Nations series, and scored four tries in the tournament. Reardon won caps for Great Britain while at Bradford Bulls in 2004 against Australia (3-matches), and New Zealand (2-matches), and won caps for England while at Bradford Bulls in 2005 against France, and New Zealand (sub). He missed the back end of the 2005 campaign with injury but made the England side at the end of the season, and toured Australia and New Zealand as a stand-by for the Great Britain squad in 2006. Paul Cullen described as the 'best kick returner in Super League' during the 2006 season, Reardon was the Warrington Wolves leading tackle-buster with 66 in his first year at the club.
Following a conviction and a pending prison sentence for assaulting his estranged wife, Stuart was released from his club contract on 9 April 2009. On the 11 April 2009, it was announced that he has been signed until the end of the season for Super League club Hull, to "add depth to the squad". Eleven days later he was released by Hull FC because he failed a medical due to an Achilles tendon injury sustained in May 2008.
In 2013 he became a face for an Australian underwear and swimwear brand, The Navy Diver www.thenavydiver.com