"This is a hugely important appointment at a significant moment in Swindon's recent history and we are delighted to appoint a football man of Kevin's calibre as our new manager," chairman Jed McCrory told the club's official website.
"He has great connections with top players and he is a proper football man. We have every faith for Kevin now to lead Swindon from the front at a pivotal moment in the campaign."
The 52-year-old, who won the double as a player with Liverpool in 1986, spent nine years as a coach at Aston Villa before his departure last year.
He takes over at Swindon with the team in fourth place in the League One table.