“There’s been a lot of external noise about Luka joining us, but he is still a young guy who will need time to adjust to the demands of playing for Brighton and the Premier League,” he added.
“We are confident that he will take this in his stride though.”
Vuskovic will replace Netherlands centre-back Jan Paul van Hecke in Hurzeler’s squad, who has moved in the opposite direction and joined Spurs on a long-term deal for £52m.
Born in Split, Vuskovic came through the academy at local club Hajduk, becoming the youngest player to feature in Croatia’s top flight when he was just 16 – and going on to become his club’s youngest goalscorer.
He was named Rookie of the Season for his impressive campaign in the Bundesliga last season, and also claimed a spot in the league’s Team of the Year.
Vuskovic has six senior caps and one goal for Croatia and made his World Cup debut against England in the group stages last month.
Brighton start the new Premier League season against Aston Villa at home on Sunday, 23 August at 14:00 BST.
