Madrid outfit Leganes, aiming to reach La Liga for the first time, must wait until the last round of matches despite beating Llagostera 2-0 at home after fellow promotion hopefuls Gimnastic de Tarragona won 3-0 at Lugo.
Alaves lead the Liga Adelante (second tier) on 74 points, while Leganes are second on 71 and Gimnastic third with 70.
The top two get automatic promotion with a third place in La Liga available via the playoffs. Gimnastic, Zaragoza, Cordoba and Girona currently occupy the playoff spots, with the games commencing after the regular season ends next week.
Alaves have spent 11 seasons in La Liga, first getting promoted in 1930.
The club's greatest moment was reaching the 2001 UEFA Cup final, losing a thrilling contest with Liverpool 5-4 after extra-time.
Alaves were last in the top flight in 2005/06, being relegated a year after promotion. The club dropped into Spain's regionalised tier in 2009, remaining there until 2013.
Their promotion means there will be four clubs from the Basque country in Spain's top flight as they join Eibar and La Liga mainstays Athletic Bilbao and Real Sociedad.
Leganes' victory saw Llagostera, the smallest team in the Liga Adelante, relegated to the regionalised Segunda Division B.
