The Tanzanian has signed a four-and-a-half-year deal, subject to a work permit and international clearance being granted, for what is understood to be an £8.5million fee.
Samatta, 27, scored 61 goals in 165 appearances during his four years with the Belgian club.
Boss Dean Smith told the official Villa 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, who has scored 10 goals for Genk in all competitions this season, including a goal at Anfield against Liverpool in the Champions League, was not registered in time to make his debut in Tuesday’s Premier League clash at home to Watford.
But Smith will be delighted to have sealed the Samatta deal given the threadbare attacking resources at his disposal.
Brazilian forward Wesley is out for the season with a knee injury, Keinan Davis has only just returned to training after three months absent with a hamstring problem, while Jonathan Kodjia has joined Qatari side Al-Gharafa.
Villa face the Hornets without a recognised striker for the fourth consecutive match and Smith admitted extra firepower was essential with his side in the relegation zone.
He said: “It’s something we’re talking about all the time.
“Suso (Jesus Garcia Pitarch, sporting director) believes the same as well. It’s something we’re looking for and looking to press on with as well.”
Smith has confirmed he would never have let Kodjia depart if there had been any doubt over landing Samatta.
“Jonathan’s had a tough season,” said Smith on the 30-year-old, who scored 31 goals in 106 appearances.
“He came back from the AFCON very, very tired after playing a summer series. Our season didn’t finished until May 27. He then got injured at Tottenham and has struggled for fitness since due to game time.
“With his contract being up at the end of the season, we hadn’t offered him a new one, and so he wanted to look at other avenues and we’ve allowed that to happen.”
Villa have also allowed Croatia goalkeeper Lovre Kalinic to leave for French Ligue 1 side Toulouse on loan until the end of the season.
Former Liverpool and Napoli goalkeeper Pepe Reina joined on loan from Inter Milan last week.
Kalinic has only made eight appearances for Vila since signing a year ago for £5.4million from Belgian club Gent, with the last of those in mid-February.
Recognising Kalinic is eager to be a part of Croatia’s Euro 2020 squad, Smith said: “He needs game time.
“He’s a Croatian national goalkeeper, with his country qualifying for the Euros. He wants to get that opportunity to play in the summer.
“I’ve got Pepe and Orjan (Nyland) who’s been in fine form for us, so his chances are limited here.”