"I am very happy and delighted a club as big as Liverpool showed interest in me," the 19-year-old told the Premier League club's official website (www.liverpoolfc.com).
"I know it's a club with a great history, great fans and a lot of great players. For me Liverpool are one of the greatest clubs in the world."
Origi began his career as a youth team player at Racing Genk before joining Lille in 2010.
He celebrated his debut for the French club with a goal against Troyes in February 2013 and has scored six times in total for the Ligue 1 club.
Origi was also on target for Belgium in their World Cup group stage match against Russia in Brazil last month.
Lille finished third in Ligue 1 last season, 18 points adrift of champions Paris St Germain.