The Southampton striker passed a medical on Saturday. The 32-year-old arrives at Anfield for a fee of just over £4 million.
There are a number of add-ons tied in to the deal, but the eventual figure will not get close to the £9m being suggested in some quarters.
Tokyo 2020
Liverpool to refuse Salah's request to play at Olympics
Lambert is already in Miami for the next stage of England's World Cup preparations alongside new Liverpool team-mates Steven Gerrard, Jordan Henderson, Glen Johnson, Daniel Sturridge and Raheem Sterling.
"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," said Lambert, who scored 117 goals in 235 appearances for Saints.
"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."
LIVERPOOL TWEET: Lambert: I can’t believe it. I’ve loved this club all my life. To be back here now is hard to describe.” #LambertLFC
The transfer has progressed quickly as Liverpool said it had to be done before the World Cup and with the player keen to rejoin the club he left as a teenager, Saints found it difficult to stand in his way given the forward's service to the club.
Lambert was born in Kirkby, Merseyside, and was a member of Liverpool's academy until his mid-teens when he was released and found himself plying his trade in the lower leagues for the likes of Macclesfield, Stockport, Rochdale and Bristol Rovers before finding success at Southampton.
He will provide some much-needed back-up to frontline strikers Luis Suarez and Daniel Sturridge at Anfield and while he may have to content himself with a supporting role from the bench, the chance to rejoin his boyhood club and play in the Champions League was an opportunity he did not want to miss.
TWEET: STAT: Liverpool now have SIX players in England's 23-man World Cup squad. That's 26%. Lallana would make it 30%. #LFC
Manager Brendan Rodgers' interest in Lambert came out of left-field while he was pursuing deals for the striker's team-mates Adam Lallana and Dejan Lovren.
Lallana was seen as the primary target to bolster the Reds' midfield, with Lovren less so for the centre of defence, but Lambert will be the first through the door at Anfield in what is expected to be a busy summer as they look to strengthen ahead of a return to the Champions League.
SOUTHAMPTON TWEET: Five seasons. 235 games. 117 goals. Countless memories. #ThankyouRickie
Liverpool have made a bid, reported to be in the region of £16million, for Sevilla left-back Alberto Moreno but are still in negotiations with the Europa League winners.
Press Association Sport understands further talks with Bayer Leverkusen midfielder Emre Can over the weekend are likely to have given a clearer idea of whether the Germany Under-21 international will also move to Merseyside.
Although there is a buy-out clause of about £10m which Liverpool are willing to meet, the player's wage demands are proving a significant stumbling block.
However, what interest the club had in Swansea goalkeeper Michel Vorm to provide competition for Simon Mignolet has cooled and they are no longer considering the Dutchman as a viable target.
Ambitious Arsenal target Sterling and Mahrez, Rice has head turned - Transfer Notebook
Premier League
Benitez on verge of becoming Everton manager - reports
17/06/2021 AT 08:35