Harri Mäki opiskeli klarinettia ensisijaisesti Kari Kriikun ja Reijo Koskisen johdolla. Valmistuttuaan  Thomas Friedlin luokalta Geneven Musiikkikonservatoriosta hän liittyi Tapiola Sinfoniettaan. Hän toimi orkesterin sooloklarinetistina vuosina 1988-2018. Hän on opettanut Sibelius-Akatemiassa vuodesta 1995, ensin tuntiopettajana, sitten klarinetin lehtorina. Vuonna 2018 hänet nimitettiin  Sibelius-Akatemian puupuhallinmusiikin professoriksi. Vuonna 2012 hänelle myönnettiin ansioistaan taiteilijana ja pedagogina Pro Musica palkinto.

Harri Mäki studied the clarinet mainly with Kari Kriikku and Reijo Koskinen in Finland. After having graduated from the class of Thomas Friedli at the Geneva Conservatory, he joined the Tapiola Sinfonietta as principal clarinetist. He also studied privately with Charles Neidich and Osmo Vänskä. He has premiered dozens of works, including clarinet concertos dedicated to him by Juhani Nuorvala and Kirmo Lintinen. He is the Professor of Woodwinds at the Sibelius Academy and was principal clarinetist of the Tapiola Sinfonietta from 1988 - 2018. Harri Mäki has appeared as a soloist and chamber musician throughout Europe, the Far East, and North and South America. Many of the students graduating from his teaching studio at the Sibelius Academy in Helsinki, Finland have succeeded in both orchestral auditions and competitions around the world. In 2012, he was honored to receive the Pro Musica Award for his merits as a performer and a teacher.