Abelardo left the club on Tuesday (AEST) after a run of just one win in its last 10 LaLiga matches of the season ended its hopes of an unlikely Champions League qualification place.
Alaves ultimately finished 11th and Abelardo decided the time was right to part ways, insisting in his farewell media conference that the club did everything they could to keep him.
The club has moved quickly to name a replacement, though, appointing former Real Sociedad coach Garitano.
The 49 year-old took charge of Leganes in 2013, guiding them from the third tier of Spanish football to La Liga for the first time ever.
He then joined Real Sociedad at the start of the 2018-2019 campaign but was dismissed in December after a run of four consecutive defeats.