GMB said it could no longer be associated with the League One side because of the Italian star's political views.
The union, the UK's third largest with 600,000 members, give the club 4,000 a season but yesterday severed its ties with Swindon after their appointment of Di Canio.
The 42-year-old, who played for Celtic from 1996 to 1997 scoring 15 goals, has faced fines for giving the Roman salute to Lazio supporters during his time with the Italian club.
In his autobiography he praised Mussolini as "basically a very principled, ethical individual".
Andy Newman, the GMB's Swindon branch secretary, said yesterday: "We have decided to end our sponsorship deal with Swindon Town, we will not be renewing our agreement with them.
He added: "We have no choice. It's unfortunate but that's the way it is."
A GMB spokesman added that it "beggars belief that Swindon could have appointed him".
The club has been relegated after finishing bottom of League One.
In a statement, the club said it was confident di Canio would build a team with the "passion, pride and professionalism" to ensure it could return to League One "at the earliest opportunity".
Interim chairman Jeremy Wray said: "I can't wait for Paolo to get here and get started."
Di Canio started his career in Italy with Lazio, Juventus, Napoli and AC Milan.
He won the Serie A title and European Super Cup and claimed runners-up medals in both the UEFA Cup and European Cup.
He was one of eight prospective managers short-listed and interviewed for the Swindon manager's post last week by Wray.
The former Scotland, Ipswich and Hearts manager George Burley is also believed to have been among those interviewed.