The 32-year-old playmaker, who played 102 NRL games for the Sharks after 89 with Penrith, lost his No.6 position to Braydon Trindall towards the end of the 2023 season.
Leigh, who won the 2023 Challenge Cup final under head coach Adrian Lam, have confirmed the signing of Moylan who is set to partner Lachlan Lam in the halves.
Leopards head of rugby Chris Chester confirmed Moylan's signing and the role of the head coach in the recruitment coup.
"Adrian got on a plane and met with Matt and his agent, Allan Gainey, face to face," Chester said.
"He was able to explain what we want as a club, what we are looking to achieve, and his own coaching philosophy.
"Matt is a world-class player and his CV speaks for itself. Everyone I've spoken to says he's an unbelievable person, and one of those who leads with his actions on the field.
"Matt will take us to the next level. He's a running half … a good goalkicker and he's a good defender.
"It's a huge statement of intent by the club and great for our town. It's huge for us as a club that we have attracted a top-quality halfback over from the NRL."
Moylan played three State of Origin games for NSW and one Test for Australia, all in 2016.
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