Costa announced the signing of Manchester United left-back Alvaro Fernandez.
The defender was on loan at the Portuguese giants since January, playing 14 games.
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Speaking to media, reported by ZeroZero, Costa said: "Alvaro is confirmed, he is another one of those talents in which we have great hope that he will have a very worthy career."
Benfica did have an option within the contract to secure him permanently, which they have done so.
The left-back spent the first half of the season on loan at Spanish side Granada.