In 2004 Wise took his Millwall side to the FA Cup final when they lost 3-0 to Manchester United, but booked themselves a place in the UFEA cup.
He left Millwall a year ago, and has played for Southampton and Coventry in the past year.
Mark Devlin said: "We are delighted that both Dennis and Gus have agreed to join the club. It is a fantastic opportunity that was presented to us and hopefully this is the start of another new journey for Swindon fans, and hopefully one that will lead us back into League One at the earliest opportunity.
"Dennis and Gus will join on three-year deals and Dennis is keen to continue playing. The paperwork is pretty much done and dusted and we hope to make an announcement confirming that on Monday at a press conference."