The 23-year-old makes a swift return to Spain following previous spells with Mallorca, Salamanca CF, Mirandes and Alaves, playing 22 times for the latter outfit last season.
Arroyo started nine Segunda Division matches as Alaves finished fourth in the table, earning a spot in the promotion playoffs and returning to La Liga via two-legged wins over Eibar and Levante.
However, Arroyo only played 18 minutes across those four contests and was an unused substitute against Levante in both of their final matches, although he started all four of his side's games during their run to the last 16 of the Copa del Rey, where they fell short against Sevilla.
The former Colombia Under-23 international joined Liverpool's academy from Fortaleza CEIF in January 2018 and signed a contract extension last year, but he is yet to play a single game for the Reds at youth or senior level.
Arroyo - who can play as a right-back or centre-back - becomes the sixth player to leave Liverpool on loan this summer after Fabio Carvalho, Calvin Ramsay, Sepp van den Berg, Harvey Davies and Owen Beck.
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