The transfer could eventually rise to 100 million euros, Benfica said in a statement, eclipsing Liverpool's club-record £75 million paid to Southampton for Dutch centre-back Virgil van Dijk in 2018.
Nunez scored 26 goals in 28 league appearances last season in
Portugal.
The 22-year-old, who was left out of Uruguay's squad for Saturday's 5-0 friendly victory over Panama, was expected to begin a medical on Monday which could take two days to complete.