The Bluebirds had already agreed a fee for the 25-year-old, believed to be around the £1.5million mark, and the formalities of the deal have been quickly wrapped up.
Brayford told Cardiff City Player: "When I heard Cardiff were interested in signing me then I was obviously very interested, especially at the prospect of playing in the Premier League and testing myself at the highest level. Derby will always be a special club to me, but this was an opportunity I couldn't ignore."
Full-back Brayford will link up with his new team-mates ahead of Saturday's friendly at Cheltenham.
The former Crewe and Burton player made 117 appearances for Derby after making the move to Pride Park in 2010. He made 43 appearances under Nigel Clough in the Championship last term.
Brayford becomes Cardiff's second summer signing, following the club-record acquisition of Danish striker Andreas Cornelius.
Cardiff are also leading the race to sign France international midfielder Etienne Capoue.
There were reports in the French media earlier this week that the Ligue 1 club had accepted a bid of around £8.6million from the Premier League newboys, but that Capoue is continuing to weight up his options.
Source: PA
Source: PA