The 33-year-old completed his move to Cardiff on Friday, signing a two-year deal at the club.
The move sees Bellamy join his hometown club for a second time after joining on loan in the 2010-11 season from Manchester City.
"When Brendan got the Liverpool job he phoned me straight away on his first day," Bellamy told Cardiff's official website. "I felt honoured that he did that and he told me that he wanted me as part of his team.
"But my mind was made up. I wanted to come home. He gave me time to change my mind, but it wasn't going to happen.
"The fans have always appreciated me at Cardiff City and it was a pleasure to be here last time around. I feel people understand me here and it's great to be back."
Bellamy has played for nine clubs in his career, making 486 appearances and scoring 165 goals.