Sky sources understand Liverpool wanted the 19-year-old to join them immediately but Lille insisted the player return to the French club on loan for another season.
Origi, who played for Belgium at the World Cup in Brazil, has scored six goals in 35 appearances for the Ligue 1 side.
Arsenal, Tottenham and Atletico Madrid were all linked with the player but he has opted to join Belgium team-mate Simon Mignolet at Anfield and become Brendan Rodgers' sixth summer signing.
Origi told the club's website: "I am very, very happy and delighted a club as big as Liverpool showed interest in me. I'm very excited.
"I know it's a club with a great history, great fans and a lot of great players. For me, Liverpool is one of the greatest clubs in the world and I'm very excited to be part of this great history.
"I am very proud to sign for the club. I'll give everything for the club, like I did when I was small and did for Lille.
"I'm hoping we can achieve great things together."
Origi follows Southampton trio Adam Lallana, Rickie Lambert and Dejan Lovren, Bayer Leverkusen midfielder Emre Can and Benfica winger Lazar Markovic to Anfield this summer.
And while he will not be part of Brendan Rodgers' plans for the coming campaign the striker cannot wait to be able to make an impression.
"The fact we have a young team and can grow is the most exciting part," he added. "With the coach we have he's a great manager who can handle a young team.
"He's said a lot of good things about Liverpool and told me it's the perfect club for me. He was only positive and it was great to be able to talk with him about Liverpool.
"We also have experienced players. I think we can go very far - we have a lot of quality in the group.
"This year I'll have a chance to play at European level, so in the Europa League or Champions League.
"It's important for me to gain a place in the team, improve and be ready for the season after that."
Watch Liverpool take on Manchester City in the International Champions Cup on Thursday morning - kick off is just after midnight, live on Sky Sports 1.
As for is Origi good enough, the club has stated they have been tracking Origi for 4 years so they know the kind of player we have just signed. Loaning him back is a good thing because it means he will continue to develop and will come to us next season with a full season of experience. I also do feel another striker signing is needed and will be made as I think Borini is on his way to Sunderland which would leave only Sturridge and Lambert. I'm reckoning we could be poised to sign Shaqiri which is more realsitic or maybe Reus.- lfcfan80