FC St. Pauli In August 2014, Budimir joined German club
FC St. Pauli of the
2. Bundesliga on a four-year deal until 2018. St. Pauli had to pay a transfer fee believed to be around €900,000. In an interview on Budimir's signing, former Croatian international
Jurica Vranješ described him as "tall, strong in the air, and reliable in combinations" and compared his style to
Dimitar Berbatov. Budimir had a tough time at St. Pauli, scoring one goal in 20 appearances in the St. Pauli shirt.
Crotone and Sampdoria On 1 September 2015, Budimir was loaned out to Italian club
Crotone for the remainder of the season. He made his Crotone debut on 7 September 2015, in a 4–0 loss to
Cagliari Calcio, coming on as a 71st-minute substitute for
Pietro De Giorgio. In March 2016, Crotone exercised their €1 million buyout option on the player. Budimir ended the season as Crotone's top goalscorer with 16 goals in 40
Serie B appearances, as they were promoted as runners-up to Cagliari; this tally was fourth for goalscorers in the whole league season. In June 2016, ahead of Crotone's debut
Serie A season,
Sampdoria of the same league activated Budimir's release clause believed to be in the region of €1.8 million, and the player signed a deal ending in mid-2020. A year later, he was sent back to Crotone on a one-year loan with obligation to buy. The obligation was fulfilled by now relegated Crotone at the end of the season, and he remained in the club on a permanent contract.
Mallorca On 15 January 2019, Budimir moved on loan to Spanish club
Mallorca. He scored his first goal for the
Balearic club on 3 February as a
Panenka penalty kick in a 2–0 home win over
AD Alcorcón, later being sent off. On 27 June, after
achieving promotion to
La Liga – he scored the opening goal as they overturned a 2–0 first-leg deficit to defeat
Deportivo de La Coruña 3–2 on aggregate in the play-off final – he signed a permanent deal for a €2.2 million fee. During the
2019–20 season Budimir scored 13 goals, On 7 June 2021, Osasuna announced the signing of Budimir on a permanent deal until June 2025. In the
2023–24 season, he became the top scorer for his club, as he also set a new personal best in La Liga by scoring 17 goals. On 2 March 2025, he scored a penalty in a 3–3 draw against
Valencia, surpassing 's long-standing record of 57 La Liga goals for Osasuna. He finished the
2024–25 season with 21 goals, setting a new personal best and eclipsing his previous season’s tally. He would also become the 3rd top La Liga scorer that season, beating out the likes of
Julian Alvarez and
Raphinha. ==International career==