The Spanish forward will return to La Liga with a view to a permanent move 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 last week and also revealed that they would have the option to buy the 26-year-old for a set price.
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.
And he admitted that 2013-14 was a poor season for him personally, telling Sevilla's official website: "It was a bad season personally, where I didn't play as much as I wanted.
"I'm happy to come here. The club put a lot of effort into getting me here.
"When we knew of the interest of the club, both my agent and I made a lot of effort to come here."
Lucas Leiva is expected to follow Aspas in leaving Anfield on loan, with Napoli close to signing the Brazil midfielder, and the Reds have agreed to sell Fabio Borini to Sunderland if personal terms with the player can be finalised.