Born in Tallinn in 1978 to parents who were both classical pianists, Randalu moved with his family to Germany at the age of nine, settling in Karlsruhe. Weaned on classical music, he discovered rock, pop, and jazz as a teenager. He attended the local music school before going on to study at the University of Music Stuttgart, the Royal Academy of Music in London, and the Manhattan School of Music. His first recorded appearance was in 2002 on Estonian singer Siiri Sisask's album Jälg. Randalu's own solo debut, Confidance, appeared in 2004 on Finetone; the following year he formed his first quartet for the album Tidbits. In 2006, he was nominated for a Grammy for his work on the Henry Mancini Institute Orchestra & Big Band's full-length Elevation. He followed with the albums Desde Manhattan (2009); Enter Denter, with the Tallinn Chamber Orchestra (2010); and Equilibrium, a duo effort with American guitarist Ben Monder on Fresh Sound New Talent (2012).