Budimir started his professional career with HNK Hajduk Split, in the season 2004–05. In January 2005, he was loaned from Hajduk Split to NK Uskok and in August 2005, he was loaned to NK Mosor. He started the season 2005–06 with Hajduk split, but he was loaned for the third time to HNK Šibenik in July 2006.
On 10 January 2007, Budimir moved to Greece and signed a four-year contract with Superleague side Ergotelis. He developed into the club's first choice striker under coach Nikos Karageorgiou, staying in Crete for six seasons, in which he appeared in 139 Superleague matches and scored 24 goals. Until his departure in 2012, after the team was relegated to the Football League, Budimir had become the club's all-time top-scorer in the Superleague, and ranked second all-time top-scorer in all domestic football competitions, behind former teammate Patrick Ogunsoto. Budimir still holds the record for most goals scored for Ergotelis in top-flight and as of 2017, ranks 4th in domestic league overall top-scorers for the club. His 139 Superleague caps for Ergotelis also rank him third in top-flight appearances for the club.
On 4 July 2012, Budimir signed a two-year contract with the Cypriot club APOEL. At the end of the season he became a champion for the first time in his career after winning the 2012–13 Cypriot First Division with the club. During his spell at APOEL, Budimir appeared in 30 league matches and scored 4 goals. On 31 December 2013, APOEL terminated Budimir's contract with the club by mutual consent.
In January 2015, Budimir signed a six-month contract with Cypriot Second Division club Enosis Neon Paralimni rejoining his former coach at Ergotelis, Nikos Karageorgiou. He appeared in 10 matches scoring 7 goals, helping the club win the championship and gain promotion to the First Division. On 22 May 2015, it was announced that Budimir had extended his contract with the club.
Budimir moved to NK Rudeš in the summer of 2017, and impressed in his first season at the club, scoring 13 goals. However, following a dispute with his manager, he terminated his contract with Rudeš.
Dinamo Zagreb
On 30 April, Budimir reportedly completed a move to Dinamo Zagreb, signing on a one-year contract. Dinamo confirmed the move on 1 May, with Budimir set to wear the No. 9 shirt, previously worn by Ángelo Henríquez. Budimir scored on his debut for the club, on 4 May, in a 2–2 draw away at Slaven Belupo.
