Cucurella impressed on loan at Ipurua last season, scoring in the 2-2 LaLiga draw with Barca on May 19.
Eibar took up the option to sign him for €2m but Barca inserted a €4m buy-back clause in that deal, which they have now activated.
It remains to be seen whether Cucurella will stay at Camp Nou for 2019-20 or be sold on to raise funds.
Sevilla and Real Betis had been linked with an interest in the player, who can operate both at full-back and as a winger.
Bundesliga clubs Eintracht Frankfurt and Borussia Monchengladbach are also rumoured to have been monitoring the Spain youth international.