The 27-year-old Tanzania international has signed a four-and-half-year deal, subject to a work permit and international clearance being granted.
He has scored 10 goals for Genk in all competitions this season including a goal at Anfield against Liverpool in the Champions League.
"I'm really pleased we have managed to bring Mbwana to the club," said Villa manager Dean Smith.
"He has scored goals throughout his career and I'm looking forward to working with him."
Samatta will be the first Tanzanian to play in the Premier League but he won't be available for Villa's home match against Watford on Tuesday.
"I'm so excited," Samatta said. "It's a huge step for me in my career. It's a big step for the country too. Everyone was looking for a Tanzanian to play in the Premier League.
"I know a lot about Aston Villa. I used to watch [Villa's record Premier League scorer] Gabby Agbonlahor when he was here."