The striker completed a move to Anfield for an undisclosed fee, returning to the club he left as a trainee 17 years ago.
Lambert scored 115 goals in 229 games for Southampton after signing from Bristol Rovers in 2009, propelling the club to the Premier League and himself into the England squad for the FIFA World Cup.
In an open letter to the south-coast club's fans after his move was confirmed, Lambert expressed huge gratitude, claiming Southampton will remain in his heart forever.
He wrote: "What can I say…?
"Southampton has been my life for the past five years, in which we have achieved all of our dreams and more.
"First I have to thank Markus Liebherr for saving Southampton then Alan Pardew for bringing me to the club.
"Thank you to all the staff involved in making me the player I am today. Without your knowledge and commitment I would not be here right now at a World Cup with England.
"Thank you to all the players, past and present, who I have had nothing but good times and success with driven by our club captain, Kelvin Davis. I love every last one of you.
"Thank you to the managers I have worked with – Alan (Pardew), Nigel (Adkins) and Mauricio (Pochettino) – and their teams for helping me and Southampton step up and adapt to every challenge that has come our way the past five years.
"When I grew up there was only one club I loved. I can honestly say now I have two clubs which will always be in my heart and that is thanks to the Saints fans.
"The people who support this club have been nothing short of amazing towards me and, when I look back in years to come, it will be the relationship I had with the fans here which will stand out the most.
"Southampton have allowed me to realise a lifelong ambition by joining Liverpool FC and taking my family home. The five-year plan when I arrived was to get this club from League 1 to the top half of the Premier League. Against all the odds we have achieved that.
"Now, under Katharina Liebherr's leadership, the club has the chance for new plan, a new chapter, and I wish them all the success in the world."
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