The striker completed his switch to Selhurst Park on Friday, arriving in London on a three-year deal for an undisclosed fee.
After starting his career with Manchester United, Campbell had spells in the top flight with Tottenham and Sunderland, before his six goals in 37 appearances failed to keep Cardiff in the Premier League last season.
Campbell is now looking forward to joining a Palace outfit that surprised many by finishing 11th in the previous campaign.
"I am delighted to sign on the dotted line and become a Crystal Palace player and now I am really looking forward to being part of this club and meeting the other lads," he told the club's official website.
"This is a great opportunity for myself to, firstly, get back in the Premier League and also have the chance to be around a great manager and some fantastic players.
"The last couple of weeks have been frustrating for me but I can't wait to get started now in the red and blue of Crystal Palace.
"Last season this club made great progress, I remember the run of games without defeat and from when Tony Pulis came in he got the club moving up the league.
"Around Christmas looking in at this club it looked like Palace were dead and buried but the gaffer breathed some fresh life into the club and added to the squad to help the team push up to 11th."
