Taiwo Awoniyi, who will immediately head out on loan to FSV Frankfurt.
The 18-year-old, who joins the Reds having previously represented Imperial Academy in Nigeria, is to spend the rest of the season on loan with the second-division German side.
Liverpool paid around £400,000 for Awoniyi’s services, according to the Press Association.
He told the club’s official website, “This is the biggest club in the world and I’m privileged to be here.
“I’ll try to develop myself very well so that when I come back to Liverpool I’ll be able to add value to the team.
“When I’m in the red shirt, I will always give my very best to make the fans happy.”
Awoniyi is a current Nigeria under-23 international. He has also played for the country at the Under-17 and Under-20 World Cups, and earned a call-up to the senior Nigeria squad in 2013.
The news of his signing comes on the same day that three players left Liverpool.