The Reds have reportedly signed Aspas on a long-term contract.
The striker has long been linked with a move to Liverpool and has now signed from the Spanish club on an undisclosed fee.
Aspas scored 12 goals for Celta Vigo last season, helping the club avoid relegation from La Liga.
The player reportedly passed a medical at the clubs Melwood training ground and the fee paid to Celta Vigo is speculated to be around £7 million.
Aspas will be the third signing that Liverpool have made this summer, having already acquired Kolo Toure on a free transfer from Manchester City and young midfielder Luis Alberto from Sevilla.
Those three could soon be joined by Sunderland goalkeeper Simon Mignolet, who is set to have a medical with the club next week, with Liverpool agreeing an £11 million fee with Sunderland.
Liverpool boss Brendan Rodgers is looking to strengthen his side this summer following a disappointing season at Anfield where the Reds managed to finish in 7th position, behind local rivals Everton.
Rodgers also looks set to sign another striker, especially if Luis Suarez leaves the club as is expected.
The Reds have been strongly linked with Aston Villa striker Christan Benteke.