Núñez's arrival comes six months after Colombia winger Luis Diaz joined from Porto, Benfica's big rival, and had an instant impact at Liverpool in the second half of last season.
Núñez is expected to become Liverpool's starting striker as a replacement for Sadio Mané, who has been heavily linked with a move to Bayern Munich.
It is an immediate response by Liverpool to the signing of another of European soccer's top strikers, Erling Haaland, by Premier League title rival Manchester City on Monday.
Núñez doesn't come with as big a reputation as Haaland but has a strong scoring record with Benfica, netting 34 goals in 41 matches last season including two against Liverpool in the Champions League.
“I've played against Liverpool and I've seen them in lots of games in the Champions League, and it's my style of play,” he said.
“There are some great players here and I think it's going to suit my style of play here.”
In a brief statement to the Portuguese stock market, Benfica said Monday the transfer sum for Núñez could rise to 100 million euros ($104 million) based on variables.
The transfer is subject to the successful granting of a work permit and international clearance.
Núñez, a tall and technically gifted striker, will offer something new to the attack of Liverpool, which has relied on the mobility of a smaller forward line containing Mohamed Salah, Mané, Roberto Firmino, Diogo Jota and Diaz.
Salah and Firmino both have one year left on their contracts.
Núñez has made 11 appearances for Uruguay and follows in the footsteps of compatriot Luis Suarez in playing for Liverpool. Suarez was at Anfield from 2011-14.
