The club confirmed a long-awaited deal for the 25-year-old Spaniard will, subject to the necessary documentation being completed, be finalised.
Aspas, brought in at a cost of about £7.7million, scored 12 goals in 34 league appearances last season and that helped Celta survive a Primera Division relegation battle.
The fact their safety was only secured on the final day of the La Liga season held up progress but negotiations were well advanced and there was never any doubt at Anfield that it would go through.
Aspas, who was identified to play alongside Luis Suarez before he began publicly courting Real Madrid, will not be the last of the summer arrivals as Liverpool are also hopeful a deal can be done for Sevilla youngster Luis Alberto.
The 20-year-old has been on loan at Barcelona B but Thursday was the deadline for the Catalan club to offer the midfielder a permanent contract.
Having tracked the youngster's progress and made it clear to his parent club they are interested in a deal Liverpool are optimistic they can add the promising talent to their ranks.
Rodgers is keen to get as much of his business done as quickly as possible and they have made a move to bring in Sporting Lisbon's 20-year-old defender Tiago Ilori while attempts are being made to secure the services of Schalke centre-back Kyriakos Papadopoulos.
Liverpool, who have already signed Kolo Toure on a free transfer, have also been linked with Sunderland goalkeeper Simon Mignolet, with the future of Jose Reina still uncertain, and Shakhtar Donetsk's Armenia midfielder Henrikh Mkhitaryan - whose capture would become more important should Suarez leave.
The club hope to offset some of their outlay by selling striker Andy Carroll to West Ham but although a £15million-plus deal has been in place for some time, the player is stalling on agreeing to the move.
- Sports & Recreation
- Luis Suarez