Barragan has made the switch from Middlesborough to Real Betis, having spent last season on loan at the Spanish club.
The 31-year-old had previously been at Middlesborough for five years, however he was sent on loan to Betis in 2017, and he will now move there on a permanent deal.
The right-back had an option to buy on his loan deal, which Betis have activated, and he has signed a deal until 2020.
July 1, 2018