Salah's contract was due to expire next summer and, the forward announced before the Champions League final that he would remain at Anfield next season.
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The Egypt international has now ended speculation surrounding his future by signing a new three-year contract at the Premier League club.
"I feel great and [am] excited to win trophies with the club. It's a happy day for everyone," he told the club's official website.
"It takes a little bit of time, I think, to renew, but now everything is done so we just need to focus on what's next.
"I think you can see in the last five or six years the team was always going [upwards]. Last season we were close to winning four, but unfortunately in the last week of the season we lost two trophies.
"I think we are in a good position to fight for everything. We have new signings as well. We just need to keep working hard, have a good vision, be positive and go for everything again."
Salah's wage demands had been a stumbling block, but a delegation flew out to meet with the player, who is still on holiday in the Mediterranean, and came to an agreement which reportedly makes the forward the highest-paid player in the club's history.
The 30-year-old scored 31 goals in all competitions for Liverpool last season and helped them win the League Cup and FA Cup.
The forward shared the Premier League Golden Boot with Tottenham Hotspur's Son Heung-Min and was named the Professional Footballers' Association Player of the Year. He also took the top honour from the Football Writers' Association.
Salah, who joined the Merseyside outfit from Italian side AS Roma in 2017 and has scored 156 goals in 254 appearances.
"This is a special treat for our supporters to enjoy their weekend even more. I'm sure there will be some celebrations for this news tonight," Liverpool manager Jurgen Klopp told the club's website on Friday.
"Really pleased -- really, really pleased. It's the best decision for us and best decision for him. He belongs with us I think. This is his club now.
"Of course it has taken a little time but that's absolutely OK and the best things are always worth waiting for anyway. Mo is one of the best players in the world; it's only normal there are things to sort when you are at his level. So big credit to Julian Ward and Mike Gordon for guiding us to this destination.
"I have no doubt Mo's best years are still to come. And that's saying something, because the first five seasons here have been the stuff of legend.
"It is just great news. It makes me smile thinking about it. He stays with us for longer and it means we can achieve more together."
Information from Associated Press and Reuters was included in this report.