Currier was born in Huntingdon, Pennsylvania, and was raised in Providence, Rhode Island, in a family of talented musicians, including his brother Nathan Currier, also a noted composer. Sebastian Currier received degrees from the Juilliard School and Manhattan School of Music. His compositions include Crossfade, written for two harps, and Microsymph, described as a "30-minute symphony compressed into 10 minutes."
Currier completed the orchestration of Stephen Albert's Symphony No. 2, part of which was unfinished at the time of Albert's death. It was subsequently recorded on Naxos Records along with Albert's Symphony No. 1 Riverrun, which won a Pulitzer Prize.
Violinist Anne-Sophie Mutter has recorded Currier's Aftersong, which the composer dedicated to her. On June 2, 2011, she also premiered his Time Machines (composed in 2007 and reworked by the composer in 2011) with the Slovak Roman Patkoló playing the contrabasso and the New York Philharmonic Orchestra, conducted by Alan Gilbert. His Piano Concerto was premiered in April 2007 by Emma Tahmizian.
Currier has received a Grawemeyer Award for Music Composition, for Static, and a 2010 Distinguished Alumni Award from Manhattan School of Music.