Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
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.
MacDonald 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 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.