The €40 million (£31.5m) signing of the versatile 23-year-old, who can play as a defensive midfielder or centre-back, brings to an end a month-long transfer saga between the Bavarian giants and The Basques.
And speaking ahead of Thursday's Europa League qualifier against HJK Helsinki, Bielsa conceded it was a big blow to lose a player of his calibre.
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He said: "Athletic lose the contribution of a fantastic player, that is the result.
"However, he virtually played no games in pre-season and the team was constructed without him.
The Argentine trainer remained philosophic by adding: "The reality is that the decision is one that everyone knows and only time will tell how it affects him and us."
Bielsa also stressed the importance of not having a bad result in the second leg of their qualifying match against the Finns, though the tie seems a foregone conclusion as the northeners take a 6-0 lead heading into the second leg.
"A good performance does not improve anything, but a bad performance would worsen the situation we are in," said the Bilbao coach.