Dalic, Croatia's most successful coach, stepped down last week after nine years in charge, after the side were knocked out of the 2026 World Cup by Portugal in the round of 32.
"I have complete confidence in our players and it is my responsibility to bring energy, ambition and determination to ensure Croatia remains among football's elite," Bilic said in a statement.
"I am genuinely happy to begin this challenge and feel fully prepared for it - as a more mature and experienced coach than in 2006, but with the same motivation and desire to see Croatia remain powerful, bold and successful."
Bilic has been out of management since leaving Saudi Pro League side Al Fateh in 2024, having overseen 36 matches during his lone season at the club.
He brings extensive experience from English football, having managed West Ham, West Bromwich Albion and Watford, where he was dismissed after a five-month spell.
He began his coaching career at Hajduk Split in 2001 after retiring as a player for the Croatian club a year earlier.
As a player, Bilic won 44 caps for Croatia and was a key member of the side that finished third at the 1998 World Cup in France.
His immediate task will be to guide Croatia to Euro 2028 qualification before turning his attention to the 2030 World Cup.