Moore joins the Cowboys on a two-year deal as a replacement for long-serving dummy-half Aaron Payne, who retired at the end of last season.
He also has been twice capped for England.
“Our coaching staff has identified Scott as a player who is very capable of doing well in the NRL,” said Peter Parr the Cowboys’ General Football Manager.
“He sees joining the Cowboys as the chance to take his game to even higher levels and we’ll do everything we can to ensure that happens.
“We’re sure he’s going to fit in well here and challenge for a place in our 17 for round one.”
Moore becomes just the second British player to sign for the Cowboys behind Welshman Johnathan Davies, who made nine appearances for the club in 1995.