The former Reds trainee, underwent a medical on Saturday after a fee of �4million ($6.7 million, 4.9 million euros) was agreed with the Saints.

He is understood to have signed a two-year contract.

Lambert has emerged as an important squad player for England and is a member of the 23-man World Cup squad currently at a training camp in Miami ahead of the tournament in Brazil.

"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," the 32-year-old said.

"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."