McLeish held talks with chief executive Paul Faulkner following Sunday's 2-0 defeat at Norwich on the final day of the season - a result which was described as "woeful" by the manager.
Sections of fans again called for the former Birmingham boss to be axed as Villa ended the campaign just two points clear of the bottom three having won only seven games.
The club confirmed on Monday afternoon that McLeish's contract had been terminated "with immediate effect" because "the club has been disappointed with this season's results, performances and the general message these have sent to our fans."
Chairman Randy Lerner told the club's official website: "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."
McLeish had to contend with slashing the wage bill following his controversial appointment last summer, which he described as "astronomical", and has been deprived of several key players through injury or illness.
The likes of record signing Darren Bent, key defender Richard Dunne and skipper Stiliyan Petrov have been sidelined for lengthy spells and McLeish has had to put the accent on youth.
McLeish always stressed it would be a season of transition after replacing Gerard Houllier, but it was still a surprise that Villa only made sure of survival last weekend.
Faulkner said: "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."
Goalkeeper Shay Given tweeted: "Sorry to see McLeish go as he is a good man. But the fans wishes have been granted so we need to respect them as they are the soul of club"