Benfica confirmed on Monday that an initial fee of €75m ($78.59m) had been agreed with Liverpool, with €25m in potential add-ons.
"I'm really happy and delighted to be here at Liverpool. It's a massive club," Nunez told Liverpoolfc.com.
"It's a pleasure to be here in Liverpool and I'm very happy to be a part of this great club.
"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. There are some great players here and I think it's going to suit my style of play here.
"As I say, I've watched quite a lot and it's a very big club and I hope I can give everything that I've got in order to help the team."
Liverpool acted quickly to see off competition from rivals Manchester United and Arsenal to sign Nunez, who joins on a six-year deal and is the second signing at Anfield this summer after Fabio Carvalho joined from Fulham last month.
Incentives in the deal range from goal-scoring landmarks up to winning the Champions League, though at least half of the potential add-ons are easily attainable should Nunez feature regularly in a Liverpool shirt. Nunez's contract will see him paid in the region of £140k ($168k) per week, in line with other recent attacking signings Luis Diaz and Diogo Jota.
The transfer is subject to international clearance and work permit approval.
Nunez began his career at Uruguayan side Penarol. He moved to Europe in 2019 for a spell at Spanish second-division side Almeria before he signing for Benfica in September 2020.
The 22-year-old attracted attention from Premier League clubs last season as he netted 34 goals in 41 appearances in all competitions and finished as the top scorer in Portugal's top flight.
The Uruguay international's arrival at Liverpool could impact the future of Sadio Mane, who has been subject to two offers from Bayern Munich, sources have told ESPN, although Liverpool rejected both.