Born in Cuba in 1983, Virelles was raised in a musical family. His father was a professional singer and songwriter; his mother a flutist in the Santiago de Cuba Symphony. He began classical studies on the piano at the age of seven, and was constantly exposed to the wide variety of musics performed on the island.

After discovering his grandfather's jazz collection as a teenager, Virelles' musical life changed direction and he began to pursue it with a passion. At 18, he emigrated to Canada. He began musical studies at Toronto's Hunter College and came under the mentorship of saxophonist Jane Bunnett. He played on several of her albums and toured with her Spirits of Havana band.

While at Hunter, Virelles studied privately with pianist Barry Harris. In 2003, he was awarded the first Oscar Peterson Prize by the great pianist himself.

In 2009, after numerous visits to New York in a professional capacity, he relocated to the city and became an active participant in its jazz scene. He gigged and recorded with musicians as varied as Wadada Leo Smith, Threadgill (whom he also studied with and claimed as one of his great influences), Horacio "El Negro" Hernandez, Ravi Coltrane, Stanley Cowell, Rudresh Mahanthappa, Miguel Zenón, Hermeto Pascoal, and Sam Rivers, to name a scant few.

In 2008, Virelles issued Motion, his debut as a bandleader, on Justin Time. It was followed by Continuum for Pi Recordings in 2011. He made his first appearance on the ECM label as part of Chris Potter's quintet on 2012's The Sirens in 2012 and in Tomasz Stanko's New York Quartet on 2013's Wislawa.

Virelles signed to ECM later that year and recorded Mboko, his leader debut for the label. The set was released in October of 2014. His sidemen included Thomas Morgan, Robert Hurst, Marcus Gilmore, and Román Díaz. It was widely celebrated as a year-end pick on many publications' year-end lists. The pianist/composer/producer took the unusual step of following it in late 2016 with Antenna, a six-track EP. The recording was created with cellist/electronicist Alexander Overington and included guest spots from Threadgill, Gilmore, Diaz, and the percussion ensemble Los Seres, among others. ~ Thom Jurek