The 17-year-old plays for the Reds' Under-23 side and scored twice for the first team in pre-season friendlies.
Kevin Stewart, a 23-year-old midfielder who has made 17 senior appearances for Liverpool, has also signed a new deal.
The third to sign is full-back Trent Alexander-Arnold, 18, who made his first-team debut against Tottenham in the EFL Cup in October.
Woodburn has opted to represent Wales at youth level despite being qualified for England.
"Ben is in those earlier stages and has a lot of developing to do still - but wow, what an exciting talent he is," said Liverpool manager Jurgen Klopp.
"All three of these players are big talents and are at different stages of their development, but it is development that is key and they must continue to learn and improve to achieve their full potential."
Highly-rated Wales youth forward Ben Woodburn has signed a new long-term contract with Liverpool.