Vladimir Kostadinović was born August 22, 1980, in Pančevo, in what was then the Socialist Federal Republic of Yugoslavia and is present-day Serbia. He began classical accordion lessons as a young child and switched to drums at eleven, after his brother Srdjan gave him his first kit. He finished primary and secondary music school in Belgrade and graduated from its jazz department for drums in the class of Miroslav Karlović, then enrolled at the University of Music and Performing Arts in Graz, Austria, graduating in 2009 with a master's degree with honors in the studio of Professor Howard Curtis. In 2002 he had also won a scholarship to Berklee College of Music in Boston. In 2008 he was named best drummer at the Tuscia in Jazz competition in Italy, judged by a jury that included Kenny Barron and Flavio Boltro, and he also won the Jimmy Woode Competition.

In August 2009 Kostadinovic performed in New York with Hammond organist Tony Monaco, and around the same time formed his own working quartet with tenor saxophonist Jimmy Greene, pianist Danny Grissett, and bassist Matt Brewer. The group went into PKRS Studio in Brooklyn on September 15, 2009, to record his originals-heavy debut as a leader, Course of Events, released in 2011 on the Austrian label Jive Music.

He subsequently based himself in Europe, joining pianist Antonio Faraò's trio in 2012 for extensive touring, and recorded his second leader album, The Left Side of Life, live on October 4, 2014, at the Generations Jazz Festival in Frauenfeld, Switzerland, with saxophonist Seamus Blake, pianist Marko Churnchetz, and bassist Joe Sanders. Released in 2016 on the German label Enja Records, the album carries a liner-note testimonial from drummer Antonio Sanchez and drew a rave from Modern Drummer, which wrote that Kostadinovic "sounds very American, but with a touch of something different."

Alongside his own bands, Kostadinovic became the regular drummer in trumpet legend Dusko Goykovich's working quintet, alongside bassist Martin Gjakonovski and pianist Renato Chicco, documented on Goykovich's The Brandenburg Concert (2013, Enja), which paired the group with a string orchestra. His profile on the American scene kept growing too: in 2023 he was the drummer on trumpeter Jim Rotondi's Criss Cross Jazz album Over Here, alongside pianist Danny Grissett and saxophonist Rick Margitza, his first credit for a label that would soon sign him as a leader.

In 2024 Criss Cross Jazz signed Kostadinovic as an exclusive artist. On September 5 of that year he convened an all-star sextet at Samurai Studios in Astoria, New York, to record Iris, named for his then-eight-year-old daughter: saxophonists Ben Wendel and, on two tracks, Chris Potter, trumpeter Alex Sipiagin, vibraphonist Joe Locke, pianist Geoffrey Keezer, and bassist Matt Brewer, produced by Jerry Teekens. Released June 27, 2025 as Criss Cross 1425, the album closes with an arrangement of Sonny Rollins's "Airegin" alongside six Kostadinovic and Locke originals. Kostadinovic's own artist biography states the album was named to DownBeat magazine's Best Albums of 2025 list, and the British jazz site ukvibe.org gave it a five-star review, calling it "one of the musical highlights of the year."

That same year, 2024, Kostadinovic also recorded as the drummer in a trio led by guitarist Roni Ben-Hur, with bassist Martin Gjakonovski, on The Abraxas Sessions, Vol. 2 (Live), a return engagement with the bassist he had already worked alongside in Goykovich's quintet a decade earlier. Vienna-based, Kostadinovic continues to tour and record on both sides of the Atlantic.

Kostadinovic's drumming blends the muscular, hard-driving postbop lineage he studied on both sides of the Atlantic with textural touches from his own Balkan background, a hybrid quality Modern Drummer singled out when it wrote that he "sounds very American, but with a touch of something different." He is as convincing inside Dusko Goykovich's trumpet-led straight-ahead quintet as he is driving the six-horn frontline of his own Iris sextet, and Criss Cross Jazz signed him as a leader on the strength of that same combination: a composer's ear (six of Iris's seven tracks are his own writing) paired with a drummer's command of dynamics across a band stacked with heavyweight horn players. Critical reception has followed accordingly: ukvibe.org's five-star review of Iris called it "one of the musical highlights of the year," and his own artist biography cites DownBeat's Best Albums of 2025 recognition for the same record.