The hero from last season's Champions League will not have a release clause in his new deal, according to Goal.
The Reds view Origi as a key player for their future after previously sounding out interest for the Belgian in January and the early parts of this summer.
"I'm very happy to be able to sign this contract and it gives you a boost at the beginning of the season, as well as the end of the season last year. So I'm very happy," Origi told liverpoolfc.com.
"I always felt comfortable here. I made steps during my career, I say that I became a man here at this club, I signed when I was 19.
"When we had to make the decision I just wanted to speak with the club first and my entourage, but the feeling was always that I wanted to stay and extend my contract.
"It's an amazing club, we have a good group, the staff are amazing. Even coming into Melwood, the people that work here and everything, you feel there is something special going on here.
"We're still young so there's a lot of potential in the group. I'm just having fun in training and on the pitch. Those are all important factors as a player."