In a statement released on Friday, the club said both players have signed five-year deals.
Shalulile said the reason he joined Sundowns is to have a shot at the Caf Champions League and win trophies.
"I joined Sundowns because I think it’s one of the best clubs in Africa and I want to win trophies. It’s a platform for me to play in Africa with the Caf Champions League," Shalulile told the Sundowns website.
Shalulile spent five years at Highlands Park between 2015 and 2020 and scored five 29 goals in 85 appearances.
Last season, the Namibia international finished the season as the league's joint-top goalscorer with 16 goals alongside Orlando Pirates marksman Gabadinho Mhango.
Mvala is also eager to win trophies with the Tshwane giants and he's already looking forward to getting the ball rolling.
"Every season Sundowns competes for trophies, which is something you want as a player, to win something for yourself, for your family, for the supporters, for everyone, I’m looking forward to meeting all the players. So, that we can share good moments and keep winning," he said.
The 26-year-old midfielder featured heavily for Owen Da Gama's side last season, making 34 appearances across all competitions.
Mvala will compete with the likes of Hlompho Kekana, Rivaldo Coetzee, Tiyani Mabunda, Andile Jali and Sammy Seabi for a place in Pitso Mosimane's team next season.
Shalulile is considered a big catch for the Brazilians, who have struggled to find the perfect number nine ince the departure of Leonardo Castro in 2018.
In the absence of a natural forward, Mosimane resorted to playing a few of his players as strikers, including Percy Tau and Lebohang Maboe.
The club brought in Mauricio Affonso at the start of the 2019-20 season but the Uruguayan struggled with injuries, scoring just a single goal in six league appearances for the Brazilians.
And the acquisition of Shalulile is set to ease the pressure on the rest of the striking department ahead of the new season, including on Themba Zwane, who finished the season as the club's top goalscorer.