"I want to play regularly and challenge Craig Gordon to be Scotland's number one," Marshall told BBC Sport.
Marshall has been very much third-choice for Scotland since making his international debut in 2004.
"I'm happy to join Cardiff and it wasn't a hard decision to make," he said after ending his two-and-a-half year spell with Norwich.
"It will be better for me playing at the top end of the Championship."
He added: "I've signed with a view to being number one.
"I played every game last season for Norwich and have been a regular for the last few years.
"I expect to work hard ready for the start of the season and prove I'm there to be the number one.
"I'm desperate to be in the team, I wouldn't have signed otherwise.
"I've had the chance to be a number two to someone a few times but I want to play games. I've also left other clubs because I wasn't playing."