The 25-year-old forward spent a loan spell with the Basque side last season but only made five appearances, scoring twice.
However, those performances have been enough to warrant a permanent move back to La Liga from Premier League parent club Man City.
Sobrino, a Real Madrid youth graduate left Spanish football in 2015 but failed to make an appearance for the Manchester-based club.
A loan spell with Catalan side Girona later followed before he moved to Alaves on loan in 2016.
Having now agreed on a move to the Mendizorrotza – Sobrino will sign a four-year contract at the club.