A club statement said Aspas passed a medical at the Red's Melwood training complex with the Spaniard inking a long-term contract - subject to international clearance.
The 25-year-old scored 12 goals and provided seven assists in 34 appearances for former club Celta Vigo last season.
Manager Brendan Rodgers' latest signing joins Spain Under-21 player Luis Alberto and former Manchester City defender Kolo Toure at Anfield.
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