Born in Finland and raised in Boston, Gregg studied under Boston Symphony violinist Aza Raykhtsaum before attending Indiana University, where he studied under Koichiro Harada and Ik-Hwan Bae. He pursued graduate studies at the Cleveland Institute of Music and Southern Methodist University, where he was a student of William Preucil and Emanuel Borok, respectively. Miika Gregg has also been mentored by Alex Kerr, with whom he studied for several summers as a fellowship recipient at the Aspen Music Festival and School.

Gregg has performed with numerous orchestras and music festivals across the country. He has held leadership positions with the Akron Symphony Orchestra, Spoleto USA Orchestra, and the Breckenridge Music Festival Orchestra, and has also performed with the Canton Symphony Orchestra, Sun Valley Summer Symphony, and San Francisco Symphony. He has also been an active chamber musician, collaborating frequently with his former colleagues in the Dallas Symphony and beyond. He enjoys spending his free time outdoors and writing songs.