The Frenchman was only appointed in November on a three-and-a-half-year deal, but has been unable to prevent their slide towards relegation.
Villa sit bottom of the Premier League, 12 points from safety with seven games remaining.
Villa said in a statement last night: “The club would like to place on record its sincere thanks to Remi for all his efforts during a difficult period and wish him well in the future.”
Eric Black will take over as acting manager until Garde’s replacement is appointed.
Garde, a former Lyon boss, won just two league games after taking over from Tim Sherwood. Villa have lost their last six and conceded 18 goals in the process.
They are nine points behind second-bottom Newcastle.
Garde was understood to be unhappy with his failure to be backed in the transfer market in January, with Villa opting not to sign a player despite his personal efforts.
The 49-year-old’s departure follows a shake-up of the Villa board since the turn of the year, with both chief executive Tom Fox and sporting director Hendrik Almstadt quitting in the past fortnight.
Chairman Steve Hollis, who took over that role from club owner Randy Lerner in January, has been conducting an internal review.
Former Football Association chairman David Bernstein and Lord Mervyn King, a former governor of the Bank of England, have recently joined the board, while ex-Villa manager Brian Little has been appointed as an advisor.