Nuñez came to the Premier League club in 2022 after making great success in the Portuguese league with Benfica.
The striker had difficulty adapting to English football and was seen early on as a flop given his price tag. Nevertheless, he scored a total of 40 goals in 143 matches for Liverpool.
"We wish him and his family the best for the future," writes Liverpool.
According to reports, the 26-year-old Uruguayan costs 600 million kronor for al-Hilal, which is owned by Saudi Arabia's investment company (Pif) – just like Newcastle.
Nuñez's transfer may pave the way for Alexander Isak to get his dream move to Liverpool, now that the club has received more money. However, the latest reports suggest that Newcastle does not want to sell Isak regardless of the bid. At the same time, coach Eddie Howe has said that he only wants players on the team "who want to be here".