Former Lyon boss Garde on Monday signed a deal until June 2019 with the midlands outfit bottom of the Barclays Premier League.
He watched his new side in their 3-1 defeat at Tottenham and will take charge of his first game in Sunday's visit of Manchester City after replacing Tim Sherwood.
Villa are four points from safety following the loss at White Hart Lane - their ninth in 11 matches this season.
But Garde said: "It is an unbelievable honour to be the manager of such an illustrious football club.
"I've had extremely positive meetings with both the owner, Randy Lerner, and chief executive Tom Fox
They have ambitious plans for the club and I'm excited that they have turned to me to help them realise them.
"Obviously we have a difficult task in front of us but I'm looking forward to the challenge with the support of everyone who loves Aston Villa."
Garde spent three years in charge at Lyon, winning the French Cup in 2012, and left for personal reasons in 2014.
He won the Premier League as as player with Arsenal in 1998 and made 45 appearances for the Gunners after joining in 1996 before retiring three years later.
The 49-year-old also played for Lyon for six years before moving to Strasbourg in 1993 and won six caps for France.
Garde joins a club in crisis after they brought in 13 new players in the summer but sacked Sherwood last month following a run of six straight defeats
There was internal tension at the club and chairman Lerner conceded they were floundering, but vowed to get it right
He said: "Remi came with ideas, honesty, humour and a steely sense of what it will take for Aston Villa to be what it is meant to be - hard-working, tireless, creative and unwilling to concede.
"Nobody at Villa can deny that we are way behind.
"We recruited aggressively this past summer and it is our responsibility to now harvest this talent rather than buckle under pressure and criticism - we are better than that
On behalf of the board, we wish Remi every success."
Fox added: "For the past year we have been working purposefully to transform the club in order to build a successful organisation that can compete and succeed in the Premier League.
"Finding a manager who shares and believes in our vision and has the ability to bring it to life through performances on the pitch is essential
We are confident that Remi is the manager who can deliver the best from the current squad and help set the club up for future success."
Source : PA