The 43-year-old Terzic will replace Ernesto Valverde, who said in March that he would leave Bilbao at the end of the current campaign after four years in charge.
Terzic was previously in charge of Borussia Dortmund, winning the German Cup in 2021 and narrowly missing out on the Bundesliga title in 2023.
He also led Dortmund to the UEFA Champions League final in 2024 but lost to Real Madrid at Wembley before leaving and has not been in management since then.
Terzic had also been Slaven Bilic's assistant at Turkish club Besiktas and English Premier League side West Ham.
The departing Valverde, who has had three tenures as Bilbao coach, ended their 40-year trophy drought when his side won the Copa del Rey in 2024.
Bilbao are currently eighth in Spain's La Liga standings with four games of the season left with Valverde looking for a strong finish to the campaign.
The Catalans increased their lead at the top of LaLiga to 11 points after beating Getafe 2-0 on Saturday, with second-place Real Madrid only managing to draw against Real Betis.
The Catalans 2-1 win over 10-man Atletico Madrid was enough to open the gap to Real Madrid in LaLiga to seven points after Los Blancos were beaten by Mallorca.
Ernesto Valverde has confirmed he will step down as Athletic Bilbao manager at the end of the season, bringing an end to his third spell in charge of the Basque side and closing a defining chapter in the club's modern history.
Hansi Flick has said having Robert Lewandowski available again is a major boost for FC Barcelona as they prepare for a demanding La Liga clash with Athletic Club.
