The 27-year-old has signed a four-and-a-half-year contract at Villa Park with the transfer subject to international clearance and work permit.
Aston Villa have played their last three games without a recognised striker after Brazilian striker Wesley was ruled out for the rest of the season with a knee injury on New Year’s Day.
Samatta made 27 appearances for Genk this season, scoring 10 goals, including one against Liverpool in the UEFA Champions League last November.
He moved to the Belgium side from TP Mazembe in 2016 and won the Belgium league title last season.
Villa boss Dean Smith told the club's official website: 'I'm really pleased we have managed to bring Mbwana to the club.'
'He has scored goals throughout his career and I'm looking forward to working with him.'
Samatta will become the first Tanzanian to play in the Premier League when he makes his Aston Villa debut.
"I'm so excited," Samatta said after completing the move.
"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."
Samatta will not be involved when Villa host Watford in the league on Tuesday as his registration was not completed on time.
