Police found 49-year-old Jürgen Brümmer at the bottom of the 55-metre-high Körsch viaduct near Stuttgart at around 3am on Tuesday.
A passer-by had alerted them after spotting an empty car on the bridge.
He left a suicide note at home, where his wife found their 15-year-old son dead in his bed in their Ostfildern-Nellingen house the same night, the Bild newspaper reported on Wednesday.
The newspaper added that police believe Brümmer killed his son before killing himself.
An accident in February 2012 had left the gymnast's son unable to walk or talk. He is believed to have been been run over by a vehicle and required full-time care.
The nine-time national gymnast championship winner and competitor at the 1988 Seoul Olympics had left the circuit and set up a physiotherapy clinic in Stuttgart, Baden-Würrtemberg, working with people suffering from physical disabilities.
He also used to train Germany's national junior team and football team the Stuttgart Kickers.
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