The former Torquay United and Port Vale player, 30, is new Swindon manager David Flitcroft's first Robins signing.
Dundee-born Robertson, who began his career at Sheffield United, can play at centre-half or right-back.
"It is a great challenge now to get Swindon back into League One," he told relegated Swindon's website.
Flitcroft added: "When we interviewed Chris and when we looked at his career, he's a solid character and he wants to move his family down here.
"All the other players we are speaking to are all of a similar ilk and they want to do that, commit to Swindon and they want to commit to our vision that we've set out on and off the field."
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Swindon Town have signed defender Chris Robertson on an undisclosed-length contract following his release by League One club AFC Wimbledon.