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.
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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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