The 32-year-old striker spoke to the club’s official website after putting pen to paper:
“I can’t believe it. I’ve loved this club all my life. I left here 17 years ago – and I haven’t stopped loving it since.
“I have always dreamt of playing for Liverpool, but I did kind of think the chance of playing for them had gone. I didn’t think the chance would come.
“I know how big Liverpool are – and it means everything to me – but I know what is important; I know it’s what I do on the pitch and the minutes I play. I know that’s what matters, and that’s what I’ll be focused on.”