The Egypt international has signed an extension until 2025, with the deal coming after strike partner and Senegal forward Sadio Mane left to join German Bundesliga giants Bayern Munich on a three-year deal last month.
"I feel great and (I am) excited to win trophies with the club. It's a happy day for everyone," Salah said in a statement on the club 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."
Salah scored 23 league goals for Liverpool last season to share the Premier League golden boot with Tottenham Hotspur's Son Heung-min.
He was named the Professional Footballers' Association Player of the Year and also took the top honour from the Football Writers' Association.
The 30-year-old scored 31 goals in all competitions for Liverpool and helped them capture the League Cup and FA Cup. They were beaten 1-0 by Real Madrid in the Champions League final in May.
Salah, who joined the Merseyside outfit from Italian side AS Roma in 2017 and has scored 156 goals in 254 appearances, would have been available to leave them on a free transfer at the end of next season.
He is now expected to lead a new-look front line for Juergen Klopp's side in the absence of Mane and Divock Origi -- who left the club -- with Uruguayan forward Darwin Nunez having joined in the close season.
"My message (to the fans) is the players in the team want to give our best next season to try to win all the trophies," Salah added. "As usual, you stay behind us and give us a big push and I'm sure we are going to win trophies again (together)."