Martin Gjakonovski was born in 1970 in Skopje, in what was then the Socialist Republic of Macedonia within Yugoslavia, into a musical family. His mother, Marija Gjakonovska, is a classically trained violinist who also sang in the jazz vocal quartet Impulsi, and his father, composer and conductor Dragan Gjakonovski-Špato, founded and led the Radio Big Band of RTV Skopje. Gjakonovski began on violin at six, switching to double bass at fourteen, and in his teens he and his father put together a family-rooted trio, Trio Spato, before he left for Germany.

In 1991 Gjakonovski enrolled at the Hochschule für Musik in Cologne, studying double bass under Rainer Linke and Dieter Manderscheid. He supplemented that formal training with masterclasses under a roster of major American bassists, including Reggie Workman, Arild Andersen, John Clayton, Mike Richmond and Eddie Gomez. He never returned to Macedonia to live, settling instead into Germany's working jazz circuit, where he built a career as one of its busiest sidemen, appearing on more than 80 recordings by the mid-2010s and roughly 200 by the following decade, often juggling twenty to thirty different working bands at once.

His most important early association was with trumpeter Dusko Goykovich, a fellow Yugoslav-born figure a generation older who became Gjakonovski's principal mentor and bandleader; they made the first of some thirteen albums together when Gjakonovski was twenty-four. Their run on the German label Enja Records includes Balkan Blue (1997), Samba Tzigane (2006), The Brandenburg Concert (2013, recorded with strings) and Latin Haze (2014, with Goykovich's Big Band RTS), and continued until Goykovich's death in 2023 at the age of 91.

Gjakonovski also spent several years as the working bassist in a piano trio led by Antonio Faraò, documented on two albums for the Italian label C.A.M. Jazz: Far Out (2003), billed to "The Far Out Quartet" with saxophonist Bob Berg and drummer Dejan Terzić and carrying liner notes contributed by Herbie Hancock, and the trio follow-up Encore (2004). He returned as Faraò's sideman a decade later on Boundaries (2015, Verve Records), alongside saxophonists Mauro Negri and Luigi Di Nunzio and drummer Mauro Beggio. A separate, long-running commitment was seven years as the bassist in pianist and entertainer Paul Kuhn's trio, documented on releases including Unforgettable Golden Jazz Classics (2009) and Live at Birdland (2010).

The rest of Gjakonovski's discography reads as a survey of the German and Central European jazz scene of the past three decades: pianist Anke Helfrich's trio, whose 2006 album Better Times Ahead features American trumpeter Roy Hargrove as a guest on three tracks; saxophonist Gerd Dudek's Coltrane tribute quartet, Out of This World (2016); pianist Andreas Feith's quartet on Surviving Flower (2020); Romanian-German saxophonist Nicolas Simion's various groups; the ZZ Quartet with guitarist Ratko Zjača, accordionist Simone Zanchini and drummer Adam Nussbaum; Project Them with vibraphonist Mark Sherman; the WDR Big Band alongside John Clayton and Jeff Hamilton; pianists Lynne Arriale and Olivia Trummer; accordionist and pianist Bojan Z; and Israeli pianist Omer Klein's groups. He now teaches double bass in the jazz department of the Hochschule für Musik Mainz. In 2024 he recorded as the bassist in a working trio with guitarist Roni Ben-Hur and drummer Vladimir Kostadinovic, released as The Abraxas Sessions, Vol. 2 (Live) on Dot Time Records.

Gjakonovski's career has been built less around a single leader catalog than around versatility: a bassist trusted by pianists, horn players and singers across post-bop, hard bop and Balkan-inflected world jazz alike, equally at home in a straight-ahead piano trio, a saxophone-led hard-bop quartet, or a big band. His playing carries the imprint of the American bassists he studied with in masterclasses, Reggie Workman, Arild Andersen, John Clayton, Mike Richmond and Eddie Gomez, but his choice of projects, particularly the long Dusko Goykovich association and its Balkan- and world-music-inflected repertoire, keeps a direct thread back to his Macedonian upbringing and his father's big-band background running through his adopted German career.