Moore joins the Premier League new-boys on a four-year deal having made 52 appearances for Uwe Rosler's side last season.
He is a product of Southampton's youth academy and had a spell at Farnborough Town before moving to Griffin Park in 2009.
Moore told the Welsh club's official website: "I'm delighted to be at Cardiff City - to play in the Premier League has always been my goal.
"It's exciting to think that I'll be working with quality goalkeepers like David Marshall and Joe Lewis on a daily basis and I know that I can develop and learn from them."
Moore becomes Malky Mackay's third signing of the close-season, after Andreas Cornelius and John Brayford were brought to the Cardiff City Stadium.
Mackay added: "We have been watching Simon for a year or so - he is a real up-and-coming goalkeeper.
"My thanks go to Brentford for the way they went about their business and we are delighted to get Simon in for the start of our season.
"He is one for the future and we have three quality senior goalkeepers in our squad."
‘Even though it was late in the game, the Arsenal fans started singing my name. It felt like the moment I announced myself as a professional footballer’: Ex-Gunners star recalls scoring first senior goal as a teenager at Highbury
'I started to drive myself crazy': Former Manchester United midfielder explains why it all went wrong for him under Erik ten Hag
