In a statement, the Premier League club said McLeish's contract had been "terminated with immediate effect".
The Scot was an unpopular appointment with many Villa fans after he oversaw city rivals Birmingham's relegation from the Premier League last term.
And he only narrowly avoided a similar fate with Villa this season, the club finishing just two points above the bottom three to stay in English football's top flight.
"The club has been disappointed with this season's results, performances and the general message these have sent to our fans," the Villa statement added.
"The board wishes to assure supporters that we are conscious in every sense that Villa expects and deserves more and we will strive to deliver this."
Villa ended the campaign with a run of nine winless matches and for the club's US-based owner Randy Lerner, never mind fans capable of recalling the Midlands side's 1982 European Cup triumph, that just wasn't good enough.
Their home form was especially dire, with just four wins at Villa Park representing a record low return in front of their own fans in a single season.
Lerner, in a message on the club's website, said: "We need to be clear and candid with ourselves and with supporters about what we have lacked in recent years.
"Compelling play and results that instil a sense of confidence that Villa is on the right track have been plainly absent.
"The most immediate action that we can take is to look carefully at our options in terms of bringing in a new manager who sees the club's potential and embraces our collective expectations."
Villa chief executive Paul Faulkner added: "We'd like to thank Alex for his hard work and efforts throughout this tough season.
"We are mindful of the club's need to prepare thoroughly for the new campaign and for the new manager to be able to begin working with the board so that he is quickly immersed in these preparations and also in the long-term objectives of the club.
"Our focus now will be driven by these imperatives and we will update when appropriate."
McLeish had to cope with reducing what he said was an "astronomical" wage bill and he was also deprived of several key players through injury or illness such as record signing Darren Bent and club captain Stiliyan Petrov.
Even so, it was still something of a surprise that Villa only made sure of their Premier League status on Sunday's final day of the season.