The 26-year-old's move to Selhurst Park had been widely speculated in the media, with both clubs confirming the deal on Friday for an undisclosed fee.
Cambell, formerly of Manchester United, moved to Sunderland in 2009, before another switch to south Wales for the second half of the 2012-13 season.
The striker's seven goals in nine appearances helped fire Cardiff to the Championship title that year, but he was unable to stop the Welsh outfit from dropping straight back to the second tier last season.
Campbell netted six times in 37 Premier League appearances as Cardiff, under Malky Mackay and then Ole Gunnar Solskjaer, ended the season bottom of the table, six points adrift of safety.
"We'd like to place on record our sincere thanks to Fraizer for his efforts in the City shirt, having joined us in January, 2013," said a brief statement on Cardiff's official website.
"We wish him the very best for his future endeavours."