The prolific 22-year-old could eventually cost Liverpool £85m with add-ons but Jurgen Klopp's side will initially part with £64m for his services.
Nunez scored in each leg when Benfica faced Liverpool in the UEFA Champions League quarterfinals this season.
The former Penarol striker joined Benfica from Almeria in September 2020 and scored 34 times across all competitions last season.
In a statement announcing an agreement with Liverpool, Benfica wrote: "In the early morning hours of this Monday (0:44 am), Sport Lisboa e Benfica - Futebol, SAD informed the Securities Market Commission (CMVM) that it had reached an agreement with Liverpool FC for the sale of all rights to the player Darwin Nuñez, for the amount of 75 million euros.
"To the CMVM, Benfica's SAD also informed that 'the agreement provides for the payment of a variable remuneration, so the global amount of the sale could reach the amount of 100 million euros'.
"It is further informed that the aforementioned agreement is dependent on the signing of the player's sports employment contract with Liverpool FC', it is further explained in the official document."
It is anticipated that Nunez will help fill the void due to be left by Sadio Mane, who is reportedly eyeing a move to German champions Bayern Munich.
