The 19-year-old forward, who impressed during Belgium's run to the quarterfinals of the World Cup, completed his transfer in the United States — where Liverpool is on a pre-season tour.
The club said he had signed a "long-term deal" without giving details. British media put the transfer fee at 10 million pounds ($17 million).
Origi, who joined Lille from Genk in 2010, says "Liverpool is one of the greatest clubs in the world and I'm very excited to be part of this great history."
Coach Brendan Rodgers told Liverpool's website that Origi "can be one of the most exciting talents in world football."