Mbandlwa garnered attention with his display in Tornado's 1-0 loss to Kaizer Chiefs in a Nedbank Cup last-32 tie in East London on Sunday, with TTM opting to secure his services.
The National First Division side are also in negotiations for ex-Chiefs man Matombo, who has failed to break through at Lidoda Duvha since his arrival in the off-season.
TTM spokesperson Livhuwani Madzuhe confirmed the capture of Mbandlwa.
"He is our player now. We have signed him," said Madzuhe.
"We are also trying to finalise the deal for Chris Matombo from Black Leopards."