Di Canio, a popular and controversial figure at West Ham United in a spell from 1999 to 2003, will take up his first coaching role since retiring three years ago.
"Paolo will complete his media commitments in Italy this weekend before flying to the UK on Monday... to complete the paperwork and be formally introduced," the club, who were relegated to League Two next season, said on their website on Friday.
Di Canio used to regularly make the headlines, receiving an 11-match ban in 1998 for shoving referee Paul Alcock to the ground after being shown a red card while playing for Sheffield Wednesday.
He was idolised by West Ham fans and scored a spectacular volley against Wimbledon in 2000 that was voted goal of the season. He also picked up a fair play award for catching the ball - rather than shooting into an open goal - so that injured Everton goalkeeper Paul Gerrard could receive treatment during a league game.
He later returned to Italy to play for Lazio, the club where his career began in 1985. He drew outrage in 2005 when he celebrated his team's derby win over AS Roma with a fascist-style salute.
His appointment by Swindon will end rumours that Di Canio could return to West Ham after manager Avram Grant was sacked on Sunday following their relegation from the Premier League.
