The Egypt international became the club’s second signing of the summer earlier this week, penning a five-year contract in a deal that could eventually make him the club’s most expensive ever player.
The Reds report the deal as being closer to £34 million with add-ons, just short of the record £35 million fee paid for Andy Carroll back in 2011, although the Serie A outfit insist it is £36.9 million up-front with a further £7 million in add-ons.
It is Salah’s second stint in the Premier League after an unsuccessful spell with Chelsea three years ago.
The wide-man almost signed for Liverpool before a haggle with his then club Basel over the transfer fee allowed Chelsea to swoop in and complete an £11 million move.
But the 25-year-old, who scored 19 goals and laid on 12 assists for Roma in his most successful season last term, is determined to prove his worth after just 19 appearances in 18 months with the Blues.
Salah "100 per-cent" a better player now than in last Premier League spell
Speaking to Liverpoolfc.com after his switch, Salah explained: "I have experience [of England]. I like to play here in the Premier League. I’m happy to be back and I’m excited."
The Reds’ new No.11, taking the number from Roberto Firmino who will switch to No.9, added that he is "100 per-cent" a better player than when he played for Chelsea, adding that "everything" has improved.
Salah, who also spent six months on loan at Fiorentina while a Chelsea player, said that even his "personality was different” because he "was a kid" at "20 or 21", insisting: "Now I’m four years older, everything is different. I have lots of experience in three clubs; I was at Chelsea, then Fiorentina and then Roma, I have good experience."
Asked if he feels he needs to prove himself on Merseyside, Salah continued: "Yes, always. Even if I see myself playing very well in one thing, I try to improve to do it better and better. I always think about the small details because I need to improve more and more."
The Egyptian is relishing the challenge of meeting expectations of his big money move, insisting that though last season was his best, he is keen to continue bettering himself.
"It was a top season [but] nothing changed, the season before I also scored 15 goals. I am improving and doing better and better every year," Salah said on last season, one he called the best of his career in a statement thanking Roma on Twitter.
But he looked forward to a "new challenge" which he insisted he is "happy to have" and is "excited" at, declaring: "It’s not easy, but I’m ready."
Salah continued: "Liverpool haven’t won the Premier League for a long time. We have a great team and very good players. I was watching the games last year and everyone was giving 100 per[cent to win something."
And on his new manager Jürgen Klopp, he said: "Everyone can see the coach gives everything. I hope to see that together we can give everything to win something for the club, for the supporters and for us."