The Reds boss praised his “General” and is convinced the 28-year-old can still get even better over the course of what, Press Association Sport understands, is a five-year contract.
“It is fantastic news but should not be a surprise to anyone – he is perfect for us and we for him, I think,” Klopp told liverpoolfc.com.
“Jordan embodies entirely what it means to be a Liverpool player in this modern era of football.
“You can tell through his actions on and off the pitch he treats representing our badge and our shirt as a privilege.
“He takes nothing for granted and strives to learn and be better for his team at all times.
“He carries a lot on his shoulders that people on the outside won’t see, but he embraces that responsibility and that leadership. He is our ‘General’ and I trust him completely.”
Henderson made his first start of the season in Saturday’s 2-1 win at Leicester which ensured Liverpool’s best opening to a campaign since 1990-91.
He had previously been restricted to three substitute appearances but that was no reflection of his standing within the team – and more to do with easing him back after his extended involvement in England’s run to the World Cup semi-finals.
“The best thing is, I think – in fact, I know – he will get even better in these coming years. And this improvement will come from a very high base already,” added Klopp.
“Jordan is so important to us and we are very fortunate as a club to have this person commit to us as he has.
“For Jordan and his wonderful young family, I am really pleased they now know they are part of our Liverpool family for an even longer time.”
Henderson moved to Anfield in the summer of 2011, assuming the role of captain from Steven Gerrard in 2015, and has made 283 appearances.
“It doesn’t seem like too long ago when I signed my first one – it feels like yesterday, really – but a lot has happened since then,” Henderson said.
“I feel it’s been a progressive journey for me throughout my time here and one I’ve enjoyed so much.
“There is no other place in the world I would rather play football. I want to be here for as long as I can be.
“I’m so privileged to have been a part of this club for so long, and hopefully even longer now.”