Cuenca joins Villarreal in a permanent transfer, having signed a five-year contract.
The youngster will spend the current season with Almeria to continue his development. Cuenca was with Barca B for the past three seasons.
Barca have announced Cuenca was sold to Villarreal for €2.5m plus €4m in bonuses. The deal includes a buy-back option plus 20 per cent of any sell-on fee.
Cuenca revealed: "I have always loved this club since I was a child. I had their shirts, scarves ... I even personalised the phone case with their crest and my name."