The 32-year old striker has departed Southampton to join the Reds for a transfer fee of £4million.
Lambert signed the two-year deal after passing a medical on Monday afternoon and was absolutely delighted to be returning to Anfield after leaving the Merseyside club to join Blackpool back in 1997.
"I can't believe it," said Lambert. "I've loved this club all my life.
"I left here 17 years ago, and I haven't stopped loving it since. To be back here now having just signed at the age of 32 is hard to describe.
"Obviously I have always dreamt of playing for Liverpool, but I did kind of think the chance of playing for them had gone.
"It was a shock when I heard Liverpool were in for me. I'm not going to say the words I said to my agent when he first told me - I thought he was lying. I've been trying to let it sink in for a week and it still hasn't.
"It's going to be hard to keep my emotions in check the first time I pull on the Liverpool shirt, I'm not going to lie. It's going to be very emotional, not just for me but also for my family."
Lambert will now link up with the England squad in Miami for pre-tournament training ahead of the Brazil World Cup which kicks off on June 12.
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