The 25-year-old has become the 12th summer signing at Villa Park, joining the club on the same day as England international Tom Heaton.
“For me to be here, it feels fantastic,” Nakamba told Aston Villa’s website.
“I’m looking forward to playing against some of the best players in the Premier League, one of the best leagues in the world.
“It’s a dream for me to be competing among the best players in the world.”
Villa head coach Dean Smith added: “Marvelous fits the criteria of the type of player we were looking for.
“He’s very mobile, he’s very good in possession, and he will fit in with our style of play.”
Nakamba is Villa’s second signing of the summer from Club Brugge, with Brazilian striker Wesley Moraes already having arrived at Villa Park in a deal worth in excess of £20m.
Nakamba represented Zimbabwe at the African Cup of Nations earlier this summer, but only featured in their opening-match defeat to Egypt as injury ruled him out of the remainder of their unsuccessful group stage campaign.