He was a long-time servant of Red Star Belgrade, where he played for eleven years. He was very much loved by Red Star fans, especially after his brother, Milko, joined bitter rivals FK Partizan. He was known for excellent defending skills, great tackling and powerful shooting. In 1989, he joined Swiss side Servette FC, where he stayed for six seasons and ended his career.
International
He made his senior debut for Yugoslavia in a December 1982European Championship qualification match against Wales and earned a total of 4 caps, scoring no goals. In 1994, just like his brother Milko, Djurovski accepted a call-up to represent the country of his birth. He made his senior debut for Macedonia in a March 1994friendly match against Slovenia in Skopje and earned a total of 7 caps, scoring all of his 3 international goals in a match against Cyprus. His final international was a June 1995 European Championship qualification match against Belgium.
Managerial career
Gjurovski commenced his coaching career at his former club Servette FC as an assistant, and remained in that position for 4 seasons, in which they won a Swiss title and finished up runner up in another 2. He left this role to take up another assistants role at his other former club Red Star Belgrade after this, and also remained in that role for 3 seasons. During this period, Red Star Belgrade won 2 league titles & 3 domestic cup titles. In November 2002, he became the new coach of FK Rad, after steering FK Radnički Obrenovac to promotion the season earlier. He left FK Rad after only 1 season, citing differences between the club board & himself. After a few years out of coaching, Gjurovski returned to Red Star Belgrade in March 2007 as head coach of Red Star Belgrade after Dušan Bajević walked out on the club. Đurovski did well and won the league title in his first season as senior coach 2006–07 season. However, the following 2007-08 started poorly from the getgo as the team struggled & just managed to qualify for the Champions League 2nd qualifying round with a lot of difficulties, beating Levadia in Belgrade 1:0 and losing in Tallinn 1:2. Gjurovski was sacked after that game. Gjurovski remained in the Red Star organization, however, moving to the position of the clubs chief scout. Just months after his sacking as head coach of Red Star Belgrade, Gjurovski was targeted for the assistants role at J1 League underachiever Nagoya Grampus. It was rumored after this that Gjurovski was ultimately sacked by then red star President Dragan Stojković due to the fact that he would be taking the senior coaching position at Nagoya & was determined to take Gjurovski with him as his number 2. After a 2-year rebuild, Stojković & Gjurovski managed to steer Nagoya to a long-awaited 2nd J-League championship. On 26 November 2013 Gjurovski was appointed as a head coach of the Macedonia national football team, but due to poor results on 7 April 2015 he was sacked. On 7 May 2017, Gjurovski has become the internal coach of Red Star Belgrade, after a departure of Miodrag Božović which is happen after a Red Star loss against Voždovac and losing the first place to Partizan.