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The captain had two years left on his deal and there was widespread surprise when it emerged last month that talks had stalled, particularly as the club were in the process of agreeing extensions with a number of team-mates.
However, any doubts have now been put to bed and the 31-year-old midfielder said: "I’m obviously very honoured and proud to continue the journey I’ve already been on here.
"It’s amazing to finally get it done and just concentrate on looking forward and what the future may hold.
"I’m in a different place of course, as a player and as a person, from when I first walked in. I’ve learned and grown a lot over my time here, and I’ve got to thank a lot of people for that.
"I’ve loved every minute of it, even when I look back at the tough times, I was still enjoying being a part of this football club. The longer I can do that, the better for me really. I want to be here as long as possible, I’ve always said that.
"To continue this journey is incredible for me and my family, and I hope the fans and the club feel the same way."
Henderson has made 394 appearances for the Reds, scoring 30 goals, since joining from Sunderland in 2011.
He led the side to Champions League glory in 2019 , the Premier League title in the following season, and has also won the Super Cup, the Club World Cup and the League Cup.
Henderson, who was named 2019-20 Football Writers’ Association Footballer of the Year, and this year awarded an MBE for services to football and charity, added: "Every year is the same, every year is the biggest challenge, the biggest season ahead. I feel as hungry as ever.
"I feel as hungry as I did when I first walked in 10 years ago, to prove to people that I deserve to be at this football club and give absolutely everything every single day for the badge, for the fans and for each other in this building.
"If we do that, I feel as though we’ve got a good chance of being successful."
Henderson is the sixth senior Liverpool player to extend his contract in the past few weeks after Trent Alexander-Arnold, Fabinho, Alisson Becker, Virgil Van Dijk and Andy Robertson.
Additional reporting by PA