The 26-year-old Frenchman is Villa manager Dean Smith’s first signing of the January transfer window.
Sanson joined Marseille from Montpellier in January 2017 and made 149 appearances for the club, scoring 23 goals.
He made 18 appearances for Marseille in the first half of the 2020/2021 season and scored two goals.
“I’m really happy to be here. I’m very proud to join the Aston Villa family, and in the future I hope we can do great things together," Sanson told his new club's website upon completing his move.
“It’s a magical club, a big club in England. When Aston Villa called me, I didn’t have to think about it for a long time – it was the best opportunity for me and my career.”
“It was a dream for me to join the Premier League since I was a little boy. I’ve seen the games and I like the intensity in the Premier League. For me, it was a dream and I’m very proud to join the Premier League with Aston Villa.”
Villa boss Smith added: “Morgan has performed consistently at the highest level in French football for a number of seasons as well as in this season’s Champions League, and is a player with the quality and experience to play in any midfield position," said Villa boss Dean Smith.
"He will add real competition for starting places and gives us more squad depth which is vital to competing successfully in the Premier League.”