The Spanish forward will return to La Liga after a difficult debut campaign at Anfield, during which he scored only one goal in all competitions.
The forward joined the Reds from Celta Vigo last summer but struggled to nail down a first-team place and made only 15 appearances in all competitions.
Sevilla announced a deal had been agreed to last week and also revealed that it would have the option to buy the 26-year-old for a set price.
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Aspas returns to Spain having previously played one season in La Liga — his final campaign with Celta — in which he scored 12 goals.
His position at Liverpool had been further weakened by Brendan Rodgers' signing of the likes of Adam Lallana, Rickie Lambert and, most recently, Lazar Markovic, although Luis Suarez has been sold.
Aspas' only goal for the club came against third-tier Oldham Athletic in the third round of the FA Cup in January.