Spaniard Pena, 27, had joined Barcelona's youth system in 2012 and debuted for their first team in 2023, after a loan spell at Galatasaray. He appeared for Barcelona in 28 LaLiga matches, earning 10 clean sheets.
When Barcelona's first-choice keeper Marc-Andre ter Stegen suffered a long-term knee injury in 2024, coach Hansi Flick turned to Pena as the German's replacement.
At Elche, Pena played 16 league games, with four clean sheets, and played a key role in holding Real Madrid to a 2-2 draw in November with a superb save to deny Kylian Mbappe.
"FC Barcelona would like to publicly thank Inaki Pena for his commitment, professionalism and dedication during his time in blaugrana and wishes him all the best," Barcelona said in a statement.