Tudor started his professional career at Hajduk Split in 1995 scoring five goals in 58 matches, being considered a revelation for his technique and ball control above the average of a defender.

[3] During his eight-year spell with the club, Tudor was in excellent form, despite injuries, and formed impressive defensive partnerships with the likes of Paolo Montero, Mark Iuliano, Gianluca Pessotto, Lilian Thuram, Ciro Ferrara, Alessandro Birindelli, Nicola Legrottaglie, Gianluca Zambrotta, Jonathan Zebina, Giorgio Chiellini and Fabio Cannavaro.

During this period, Juventus had one of the strongest teams in the world, and Tudor contributed well, with over 150 total appearances for the club, scoring nearly 20 goals, as a centreback.

Constantly struggling with injuries and mysterious bacterial infection of his ankle, Tudor was almost forced to end his career in 2007, but in June 2007 he decided to join his former club Hajduk Split after not renewing his contract with Juventus.

Tudor made his debut in Croatia's final match of the 1998 FIFA World Cup qualifying, a 1–1 draw at Ukraine on 15 November 1997, coming on as a substitute for Aljoša Asanović in the 89th minute.

At the tournament, he made three appearances as a substitute in the closing stages of Croatia's games against Japan, Romania and the Netherlands.

After the 1998 World Cup, he made four appearances in the Croatian national team's unsuccessful qualifying campaign for UEFA Euro 2000, being in the starting line-up on all four occasions.

He also appeared in six matches during Croatia's qualifying campaign for the 2002 World Cup, but missed the final tournament in South Korea and Japan due to an injury.

In his first appearance at the tournament, a 2–2 draw against France, he scored an own goal to put the French side 1–0 up midway through the first half.

Tudor was also included in Croatia's 23-man squad for the 2006 World Cup finals in Germany, having appeared in eight qualifying matches for the tournament, scoring two goals.

Tudor was a large, hard-working, strong and imposing defender who excelled in the air, making him a dangerous goal threat during set pieces.

[2] Tudor was hired by Hajduk Split in August 2009 to be the assistant manager to Edoardo Reja who then took charge of the Croatian giant.

After taking charge of the U-17 squad, he went to spend some time at the Juventus Center in order to improve his managerial skills with Antonio Conte.

He lost his first away match against RNK Split, but in the 2012–13 Croatian Cup final first leg he defeated Lokomotiva 2–1 on Poljud.

On 15 February 2017, Tudor was hired as the new manager of Turkish side Galatasaray, signing a one-and-a-half-year contract with the club.

[23] On 23 August 2020, Tudor resigned from Hajduk Split,[24] accepting Andrea Pirlo's offer to be his assistant at Serie A side Juventus.

[26] On 14 September 2021, Tudor was appointed at the helm of Serie A club Hellas Verona in place of Eusebio Di Francesco.

Describing his preferred style of play whilst manager of Marseille, he said “I want courageous and intensive football, not only uniquely based on the defence.