The 24-year-old signed a long term contract at his new club, after successfully completing a medical and agreeing personal terms.
Mané becomes Jürgen Klopp's fourth signing at the club, following new 'keeper Loris Karius, Joel Matip and Marko Grujic all signing for the Reds already.
One of the biggest clubs in Europe
After putting his pen to paper, Mané said: “Today is a big day and I am very happy to sign for one of the biggest clubs in Europe."
He credited Liverpool as a team "that has won a lot of trophies" and one which also has claim to "a big history".
The winger admitted he is "looking forward" to getting to know his team-mates and those around the club, as well as "starting the season".
Mané joined Southampton two years ago and during his spell at St Mary's he managed to score 25 goals in all competitions.
Klopp a key factor in transfer
Continuing to speak, he said: “I knew Liverpool were interested in me, I had some [other] opportunities, but I think for me this is the right club."
He believes that Klopp is "the right coach" and that presented "the right moment to change", before adding: “I am very happy to be a part of Liverpool Football Club."
The Klopp effect was in full flow, it seems: “He [Klopp] said he wanted me to come to play for Liverpool."
The winger continued, "I didn’t even have to ask myself, I said straight away ‘yes, I am interested’ because I know Liverpool."
Mané concluded, “I am convinced Liverpool are the right club for me with the right coach.” There is much confusion about how much the Reds have paid for their new arrival.
Liverpool insist the fee is closer to £30 million, whilst the Saints say the fee is closer £36 million. This would make him the Reds new most expensive signing after Andy Carroll.
The Senegal forward will now join up with his new squad on Saturday, when the Reds begin their pre-season training.