Luton have signed former Peterborough and Brighton striker Craig Mackail-Smith on a two-year deal.
Norwich City have completed the signing of goalkeeper Jake Kean following his release from Blackburn Rovers.
City manager Malky Mackay had previously confirmed a deal had been agreed with the Bees, with the 23-year-old becoming a Bluebird on Monday after the necessary paperwork was completed.
Moore told Cardiff City Player: "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 is set to be quickly reunited with his former team-mates as Cardiff travel to face Brentford in a pre-season friendly on Tuesday night.
Moore started his career in the Southampton academy and had a spell with Farnborough Town before joining Brentford in 2009. He kept 13 clean sheets in 52 appearances last term.
Mackay said: "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.''
Moore becomes Cardiff's third summer acquisition as the club prepare for their maiden Premier League season, striker Andreas Cornelius and defender John Brayford having already arrived at Cardiff City Stadium.