Sky sources understand the deal will keep the England midfielder at Anfield for five more years.
Henderson, a £20m signing from Sunderland in 2011, will remain at the club until 2020 and is the latest first-team player to commit his future following the renewals of Daniel Sturridge and Philippe Coutinho earlier this season.
The 24-year-old is Liverpool’s vice captain and has been tipped to become the club skipper when Steven Gerrard leaves for Major League Soccer in the summer.
Henderson was a key player for the Reds last year as they challenged for the Premier League title and has established himself as an England international.
Liverpool are also understood to be close to completing new deals for Martin Skrtel and Jordon Ibe.
Henderson said: “There has been talk about it for a while now. I’m over the moon that it’s finally done.
“It’s brilliant news for me to commit my future to this football club – I really feel that it’s a good time for us to look forward to the future, with the squad we’ve got, the manager, the size of the club and the fans we’ve got. I really think, over the next few years, we can challenge and start winning trophies.
“That’s the next phase; we’ve improved massively over the last few years, and I think the next phase for us is to start challenging for titles and trophies as well.”
Manager Brendan Rodgers believes Henderson signing a new contract should be taken as a sign that the future is bright at Anfield after a disappointing few weeks which has seen their top-four challenge falter and their FA Cup hopes end with defeat to Aston Villa in Sunday’s Wembley semi-final.
Rodgers told the club’s website: “Jordan is a brilliant professional and his dedication to his career and football in general makes him a role model to all young players.
“He has faced adversity in his time at Liverpool, but his improvement, growth and development is entirely down to his own hunger, commitment and willingness to learn and be better.
“The fact he has made such a long-term commitment to Liverpool is a sign of his belief in what we are looking to do here.
“He will have a crucial role to play as we look to take this side forward and look to add success to the progress we have made.
“I am very excited about our future and what this group can achieve together; today’s announcement is another important positive step forward.
“The owners are committed to creating a team that can grow, improve and ultimately win together.
“We have seen some very important contract renewals this season and I’m confident, under (chief executive) Ian Ayre’s stewardship, we will see further commitments made and more exciting talent secured and added to our squad.”