Moseley-born Gittens joined the Saints in 1985 before moving to Swindon, where the defender made 165 appearances, forming a solid partnership with Colin Calderwood.
Gittens helped the Robins win the Division Two play-off final in 1990, but the club were denied promotion to the top flight because of financial irregularities.
The centre-back returned to Southampton in March 1991 and also had a spell in the Premiership at Middlesbrough before moving to Portsmouth in 1993.
Gittens later played for Torquay, Exeter and Nuneaton before retiring and taking up the manager's job at Fareham.
Swindon posted a tribute on their official Twitter feed which read: "The club is devastated to hear news of the passing of former defender, Jon Gittens.
"Jon made 165 appearances for the club between 1987 and 1991, achieving promotion in 1990. Gone too soon. Never forgotten."
Southampton added on social media: "We are extremely saddened to hear of the passing of former £SaintsFC player Jon Gittens, aged 55. Everyone at the club sends their condolences to Jon's family and friends at this time."
Portsmouth said in a statement: "The thoughts of everyone at Portsmouth Football Club are with Jon's family and friends at this difficult time."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies