Matip, whose existing deal was due to expire next summer, has established himself as first-choice centre-back alongside Virgil Van Dijk this season despite strong competition from Joe Gomez and Dejan Lovren.
The PA news agency understands the 28-year-old former Cameroon international, who started in the Champions League final victory over Tottenham in June, is now under contract until 2024.
"We have a young and talented team and I think every one of us is hungry. Now we've seen how it is to win something (the Champions League) and we want to have that feeling again," Matip told liverpoolfc.com.
"There are a lot of things still to achieve. You never know how it will end, you just have to work hard and do the best you can do. Then we will see.
"It is an honour to be a part of the club. It makes me happy that people think I've done a good job and they want to keep me."
Manager Jurgen Klopp recently said he felt Matip's signing – a pre-contract deal was initially agreed in February of 2016 for him to join that summer when he became a free agent – was one of the best pieces of business done by the club.
The future did not look so rosy 12 months ago with the centre-back, who is set to return to the side for Sunday's trip to Manchester United after missing the last two matches with injury, having started just three times at this stage of the campaign.
However, he got back into the team in December and never looked back and even this season, when it seemed likely Gomez would take his place in the starting line-up, he has improved again to establish himself as first choice.
"Joel's journey at Liverpool is one I love and I am absolutely delighted he has shown his commitment to us by signing this new long-term contract," said Klopp.
"As the team has evolved and become better, so too has Joel.
"Of course, it is not easy for any player coming to the Premier League, let alone coming to a club the size of Liverpool, so maybe in the beginning there were some questions externally about his consistency. But not any more.
"Joel has been operating as a world-class centre-half throughout this year and long may it continue.
"I haven't seen many in his position performing with the consistency and quality he has been."