The 24-year-old completed his big-money transfer on Tuesday afternoon, becoming the fourth arrival of the summer for Klopp.
Mane joins Marko Grujic, Joel Matip and Loris Karius at Melwood ahead of 2016/17, and is poised to take up a key role in the Reds’ attacking line.
Scoring twice in Southampton’s 3-2 comeback win over Liverpool in March, Mane provided a showcase of his talents, reinforcing Klopp’s belief that he would make a strong addition.
Speaking to LFCTV after signing a five-year deal with the Anfield club, Mane referenced Klopp’s influence on his move.
“I had some [other] opportunities but it’s the right club, the right coach and the right moment to change,” he said.
“I’m very happy to be a part of Liverpool Football Club.
“He [Klopp] played a big role in my coming to Liverpool, and I’m looking forward to working harder and to give my best for the club.
“I didn’t even need to ask myself, I said straight away ‘yes I’m interested’, as I’m convinced Liverpool is the right club for me, and the right coach as well.”