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No option to buy has been included in the final deal, with Barcaconfirming the 23-year-old's departure via their official website on Wednesday.
The midfielder was reduced to a bit-part role in the squad after returning from a loan spell at Real Betis in the summer, but will now have the chance to continue his development in the Spanish capital.
Alena will join a Getafe side currently languishingdown in 16th in the Liga standings, and could make his debut when they take in a trip to Elche on Sunday.
The former Spain Under-21 international looked destined to become a key player at Barca after racking up 27 appearances in all competitions during the 2018-19 season.
He helped the Blaugrana win their 26th league title, but was ultimatelyunable to kick on from there, with Betis eventually offering him the chance to reignite his career in January 2020.
Alena scored once in 17 outings for the Andalusian club, who decided against trying to bring him onto their books permanently in the last transfer window.
Despite his struggles for form at Camp Nou, the young playmaker revealed back in November that he would like to see out his playing days in Catalunya.
"I want to stay, if it was down to me, I would stay here all my life," he said.