The French striker is set to sign for the Merseysiders next week after finalising terms with the club.
The arrival of Remy, 27, will lift Liverpool's spending this summer to nearly £70m, just short of the club-record fee received from Barcelona for Luis Suarez.
Manager Brendan Rodgers already has brought former Southampton duo Adam Lallana and Rickie Lambert, winger Lazar Markovic and midfielder Emre Can to Anfield.
Belgian teenager Divock Origi, who is also a striker, will return to Lille on loan after completing his 12 million euro switch.
Liverpool had emerged as the favorite to sign Remy on Friday after Tottenham pulled out of the race to capture the forward, who scored 14 goals in 26 Premier League appearances during a productive loan spell at Newcastle United last season.
Arsenal also had been strongly linked with the Frenchman, but it is understood that he was never seriously considered as an option by Arsene Wenger.
Remy is likely to join Lambert in providing back-up to Rodgers' first-choice spearhead Daniel Sturridge next season.
Liverpool also has explored the possibility of signing Wilfried Bony but is put off by Swansea City's asking price for the Cote d'Ivoire striker.