The 33-year-old revealed his departure for home-town Cardiff was an emotional decision, and he persuaded his fellow Wales international to move to Anfield while on Olympic duty
The 22-year-old followed manager Brendan Rodgers to Anfield from Swansea, sealing his move after a successful debut Premier League season was capped by representing Team GB at the Olympics.
Bellamy joined him at the Games, and told the club’s official website: "I spent the last three weeks hounding Joe Allen to go to Liverpool.
"They have got an immense player. Joe, Brendan and Liverpool will all be great winners out of this. It has been a pleasure to spend the last few weeks with him."
The midfielder has previously spoken of his enjoyment at playing under Rodgers, while he will also reduce the side’s reliance on Lucas Leiva, without whom the Reds suffered when he sustained a cruciate knee ligament injury midway through last season.
Bellamy, 33, agreed a two-year-deal with home-town club Cardiff on Friday, after previously spending the 2010-11 season on loan there, adding that leaving the Reds was an emotional decision.
"The hardest thing for me was leaving Liverpool," he admitted. "I am a Liverpool fan. I'm also a huge fan of Brendan and I think Liverpool will do great under him.
"But even that couldn't tempt me. It just wasn't going to happen for me.
"The supporters at Liverpool have been immense and the way they have been with me about this has been amazing. But my mind was made up. I am doing it for the right reasons."