The 52-year-old, who was caretaker manager at Aston Villa in 2010, has been handed the reigns at the County Ground after Paolo Di Canio resigned last week.
McDonald inherits a Swindon side who are fourth in npower League One and just three points behind leaders Doncaster and will be in charge of Saturday's trip to Coventry.
"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," said chairman Jed McCrory, who took over the Wiltshire club earlier this month.
"This is a clear message that the new board is determined to drive on for promotion this season and continue to try and bring success to Swindon.
"Kevin has fantastic football credentials as a double-winner with Liverpool during his playing days and he is an excellent coach.
"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.
"It is a new start for Kevin and for our new board of Directors and we move forward together with every confidence."
MacDonald, a midfielder in his playing days, was a member of the 1986 double-winning side at Liverpool, while he was involved with the Ireland set-up during Steve Staunton's reign.
- Sports & Recreation
- Paolo Di Canio